Algebra
Sets, Relations and FunctionsLogarithmsQuadratic Equations and InequalitiesSequence And SeriesBinomial TheoremMatricesDeterminantsPermutations and CombinationsProbabilityComplex NumbersVector AlgebraThree Dimensional GeometryStatisticsTrigonometry
Trigonometric Angles and EquationsInverse Trigonometric FunctionHeight and DistanceProperties of TrianglesCoordinate Geometry
Coordinate System and Straight LineCircleParabolaEllipseHyperbolaConic SectionCalculus
FunctionsLimit, Continuity and DifferentiabilityDifferentiationApplication of DerivativesIndefinite IntegrationDefinite IntegrationArea Under The CurvesDifferential EquationsProbability
Practice QuestionsMCQ (Single Correct Answer)
1
Three digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that the product is odd?
NDA 2015 Paper 2
2
Two events A and B are such that P (not B) = 0.8, P (A $$\cup$$ B) = 0.5 and P (A / B) = 0.4. Then, P(A) is equal to
NDA 2015 Paper 2
3
If mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1, is
NDA 2015 Paper 2
4
Seven unbiased coins are tossed 128 times. In how many throws would you find at least three heads?
NDA 2015 Paper 2
5
A coin is tossed five times. What is the probability that heads are observed more than three times ?
NDA 2015 Paper 2
6
An unbiased coin is tossed until the first head appears or until four tosses are completed, whichever happens earlier. Which of the following statement(s) is/are correct?
1. The probability that no head is observed is $${1 \over {16}}$$.
2. The probability that the experiment ends with three tosses is $${1 \over {8}}$$.
Select the correct answer using the code given below.
1. The probability that no head is observed is $${1 \over {16}}$$.
2. The probability that the experiment ends with three tosses is $${1 \over {8}}$$.
Select the correct answer using the code given below.
NDA 2015 Paper 2
7
If x$$\in$$[0, 5], then what is the probability that x2 $$-$$ 3x + 2 $$\ge$$ 0 ?
NDA 2015 Paper 2
8
A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black, is
NDA 2015 Paper 2
9
A problem in Statistics is given to three students A, B and C whose chances of solving it independently are $${1 \over 2}$$, $${1 \over 3}$$ and $${1 \over 4}$$, respectively. The probability that the problem will be solved, is
NDA 2015 Paper 2
10
An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident involving a scooter driver, car driver and a truck driver are 0.01, 0.03 and 0.15, respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver, is
NDA 2015 Paper 2
11
A coin is tossed 5 times. The probability that tail appears an odd number of times, is
NDA 2015 Paper 2
12
What is the probability that the sum of any two different single digit natural numbers is a prime number?
NDA 2015 Paper 2
13
A special dice with numbers 1, $$-$$1, 2, $$-$$2, 0 and 3 is thrown thrice. What is the probability that the sum of the numbers occurring on the upper face is zero ?
NDA 2016 Paper 2
14
There is 25% chance that it rains on any particular day. What is the probability that there is at least one rainy day within a period of 7 days?
NDA 2016 Paper 2
15
A salesman has a 70% chance to sell a product to any customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will sell the product to customer A or B ?
NDA 2016 Paper 2
16
A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or I, III or all the three. The probabilities of the student passing in tests I, II and III are m, n and 1/2 respectively. If the probability of the student to be successful is 1/2, then which one of the following is correct?
NDA 2016 Paper 2
17
The candidates solve a question. Odds in favour of the correct answer are 5 : 2, 4 : 3, and 3 : 4 respectively for the three candidates. What is the probability that at least two of them solve the question correctly?
NDA 2016 Paper 2
18
A medicine is known to be 75% effective to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is cured by this medicine?
NDA 2016 Paper 2
19
For two events A and B, it is given that $$P(A) = {3 \over {5}}$$ $$P(B) = {3 \over {10}}$$ and $$P(A/B) = {2 \over 3}$$. If $$\overline A $$ and $$\overline B $$ are the complementary events of A and B, then what is $$P(\overline A /\overline B )$$ equal to ?
NDA 2016 Paper 2
20
A machine had three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?
NDA 2016 Paper 2
21
Three independent events, A1, A2 and A3 occur with probabilities $$P({A_i}) = {1 \over {1 + i}}$$, i = 1, 2, 3. What is the probability that at least one of the three events occurs?
NDA 2016 Paper 2
22
A coin is tossed three times. Consider the following events.
A : No head appears.
B : Exactly one head appears.
C : At least two heads appear.
Which one of the following is correct?
A : No head appears.
B : Exactly one head appears.
C : At least two heads appear.
Which one of the following is correct?
NDA 2016 Paper 2
23
In a series of 3 one-day cricket matches between teams A and B of a college, the probability of team A winning or drawing are 1/3 and 1/6 respectively. If a win, loss or draw gives 2, 0 and 1 point respectively, then what is the probability that team A will score 5 points in the series ?
NDA 2016 Paper 2
24
Let the random variable X follow B (6, p). If 16 P(X = 4) = P (X = 2), then what is the value of p?
NDA 2016 Paper 2
25
A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times ?
NDA 2016 Paper 1
26
Three dice are thrown simultaneously. What is the probability that the sum on the three faces is at least 5 ?
NDA 2016 Paper 1
27
Two independent events A and B have P(A) = $${1 \over 3}$$ and P(B) = $${3 \over 4}$$. What is the probability that exactly one of the two events A or B occurs?
NDA 2016 Paper 1
28
A coin is tossed three times. What is the probability of getting head and tail alternately?
NDA 2016 Paper 1
29
A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is queen of spade?
NDA 2016 Paper 1
30
If two dice are thrown, then what is the probability that the sum on the two faces is greater than or equal to 4?
NDA 2016 Paper 1
31
A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired, so that there is at least an 80% probability that the target is hit?
NDA 2016 Paper 1
32
For two mutually exclusive events A and B, P(A) = 0.2 and P($$\overline A $$ $$\cap$$ $$\overline B $$) = 0.3. What is P(A / (A $$\cup$$ B)) equal to ?
NDA 2016 Paper 1
33
What is the probability of 5 Sunday in the month of December ?
NDA 2016 Paper 1
34
A point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge of the rectangle?
NDA 2016 Paper 1
35
A committee of two persons is selected from two men and two women. The probability that the committee will have exactly one woman is
NDA 2017 Paper 2
36
Let a die be loaded in such a way that even faces are twice likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?
NDA 2017 Paper 2
37
Let the sample space consist of non-negative integers up to 50, X denote the numbers which are multiplies of 3 and Y denote the odd numbers. Which of the following is/are correct?
1. P(X) = $${8 \over {25}}$$
2. P(Y) = $${1 \over {2}}$$
Select the correct answer using the code given below.
1. P(X) = $${8 \over {25}}$$
2. P(Y) = $${1 \over {2}}$$
Select the correct answer using the code given below.
NDA 2017 Paper 2
38
For two events A and B, let $$P(A) = {1 \over 2}$$, $$P(A \cup B) = {2 \over 3}$$ and $$P(A \cap B) = {1 \over 6}$$. What is $$P(\overline A \cap B)$$ equal to ?
NDA 2017 Paper 2
39
Let A and B be two events with $$P(A) = {1 \over 3}$$, $$P(B) = {1 \over 6}$$ and $$P(A \cap B) = {1 \over {12}}$$. What is $$P(B\,|\,\overline A )$$ equal to ?
NDA 2017 Paper 2
40
In a binomial distribution, the mean is $${2 \over 3}$$ and the variance is $${5 \over 9}$$. What is the probability that X = 2 ?
NDA 2017 Paper 2
41
The probability that a ship safely reaches a port is $${1 \over 3}$$. The probability that out of 5 ships, at least 4 ships would arrive safely is
NDA 2017 Paper 2
42
What is the probability that at least two persons out of a group of three persons were born in the same month (disregard year) ?
NDA 2017 Paper 2
43
If $$P(B) = {3 \over 4}$$, $$P(A \cap B \cap \overline C ) = {1 \over 3}$$ and $$P(\overline A \cap B \cap \overline C ) = {1 \over 3}$$, then what is $$P(B \cap C)$$ equal to ?
NDA 2017 Paper 2
44
In a multiple-choice test, an examinee either knows the correct answer with probability p, or guesses with probability 1 $$-$$ p. The probability of answering a question correctly is $${1 \over m}$$, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is
NDA 2017 Paper 2
45
Five sticks of length 1, 3, 5, 7 and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can form a triangle?
NDA 2017 Paper 2
46
A committee of two persons is constituted from two men and two women. What is the probability that the committee will have only women?
NDA 2017 Paper 1
47
A question is given to three students A, B and C whose chances of solving it are $${1 \over 2}$$, $${1 \over 3}$$ and $${1 \over 4}$$ respectively. What is the probability that the question will be solved?
NDA 2017 Paper 1
48
For two dependent events A and B, it is given that P(A) = 0.2 and P(B) = 0.5. If A $$ \subseteq $$ B, then the values of conditional probabilities P(A / B) and P(B / A) are respectively
NDA 2017 Paper 1
49
A card is drawn from a well-shuffled ordinary deck of 52 cards. What is the probability that it is an ace?
NDA 2017 Paper 1
50
Consider the following statements :
1. Two events are mutually exclusive if the occurrence of one event prevents the occurrence of the other.
2. The probability of the union of two mutually exclusive events is the sum of their individual probabilities.
Which of the above statement is/are correct?
1. Two events are mutually exclusive if the occurrence of one event prevents the occurrence of the other.
2. The probability of the union of two mutually exclusive events is the sum of their individual probabilities.
Which of the above statement is/are correct?
NDA 2017 Paper 1
51
If two fair dice are thrown, then what is the probability that the sum is neither 8 nor 9 ?
NDA 2017 Paper 1
52
Let A and B are two mutually exclusive events with $$P(A) = {1 \over 3}$$ and $$P(B) = {1 \over 4}$$. What is the value of $$P(\overline A \cap \overline B )$$ ?
NDA 2017 Paper 1
53
The mean and standard deviation of a binomial distribution are 12 and 2 respectively. What is the number of trials ?
NDA 2017 Paper 1
54
If two dice are thrown and at least one of the dice shows 5, then the probability that the sum is 10 or more is
NDA 2018 Paper 2
55
Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P(B) = 1.5 P(A) and P(C) = 0.5 P(B), then P(A) is equal to
NDA 2018 Paper 2
56
In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25%, 35% and 40% of the factory's total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X?
NDA 2018 Paper 2
57
8 coins are tossed simultaneously. The probability of getting at least 6 heads is
NDA 2018 Paper 2
58
Three groups of children contain 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One child is selected at random from each group. The probability that the three selected consist of 1 girl and 2 boys is
NDA 2018 Paper 2
59
If probability of simultaneous occurrence of two events A and B is p and the probability that exactly one of A, B occurs is q, then which of the following is/are correct?
1. P($$\overline A $$) + P($$\overline B $$) = 2 $$-$$ 2p $$-$$ q
2. P($$\overline A $$ $$\cap$$ $$\overline B $$) = 1 $$-$$ p $$-$$ q
Select the correct answer using the code given below.
1. P($$\overline A $$) + P($$\overline B $$) = 2 $$-$$ 2p $$-$$ q
2. P($$\overline A $$ $$\cap$$ $$\overline B $$) = 1 $$-$$ p $$-$$ q
Select the correct answer using the code given below.
NDA 2018 Paper 2
60
Two integers x and y are chosen with replacement from the set [0, 1, 2, ........., 10]. The probability that | x $$-$$ y | > 5 is
NDA 2018 Paper 2
61
Three dice having digits 1, 2, 3, 4, 5 and 6 on their faces are marked I, II, and III and rolled. Let x, y and z represent the number on die-I, die-II and die-III, respectively. What is the number of possible outcomes such that x > y > z ?
NDA 2018 Paper 2
62
In a binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials ?
NDA 2018 Paper 1
63
Consider the following statements
I. P($$\overline A $$ $$\cup$$ B) = P($$\overline A $$) + P(B) $$-$$ P($$\overline A $$ $$\cap$$ B)
II. P(A $$\cap$$ $$\overline B $$) = P(B) $$-$$ P(A $$\cap$$ B)
III. P(A $$\cap$$ B) = P(B) P(A / B)
Which of the above statements are correct?
I. P($$\overline A $$ $$\cup$$ B) = P($$\overline A $$) + P(B) $$-$$ P($$\overline A $$ $$\cap$$ B)
II. P(A $$\cap$$ $$\overline B $$) = P(B) $$-$$ P(A $$\cap$$ B)
III. P(A $$\cap$$ B) = P(B) P(A / B)
Which of the above statements are correct?
NDA 2018 Paper 1
64
The probabilities that a student will solve Question A and Question B are 0.4 and 0.5 respectively. What is the probability that he solves at least one of the two questions ?
NDA 2018 Paper 1
65
Two fair dice are rolled. What is the probability of getting a sum of 7 ?
NDA 2018 Paper 1
66
If A and B are two events such that 2P(A) = 3P(B), where 0 < P(A) < P(B) < 1, then which one of the following is correct?
NDA 2018 Paper 1
67
A box has ten chits numbered 0, 1, 2, 3, ......., 9. First, one chit is drawn at random and kept aside. From the remaining, a second chit is drawn at random. What is the probability that the second chit drawn is "9" ?
NDA 2018 Paper 1
68
One bag contains 3 white and 2 black balls, another bag contains 5 white and 3 black balls. If a bag is chosen at random and a ball is drawn from it, what is the chance that it is white?
NDA 2018 Paper 1
69
Consider the following in respect to two events A and B
I. P(A occurs but not B) = P(A) $$-$$ P(B) if B $$ \subset $$ A
II. P(A alone or B alone occurs) = P(A) + P(B) $$-$$ P(A $$\cap$$ B)
III. P(A $$\cup$$ B) = P(A) + P(B) if A and B are mutually exclusive
Which of the above is/are correct?
I. P(A occurs but not B) = P(A) $$-$$ P(B) if B $$ \subset $$ A
II. P(A alone or B alone occurs) = P(A) + P(B) $$-$$ P(A $$\cap$$ B)
III. P(A $$\cup$$ B) = P(A) + P(B) if A and B are mutually exclusive
Which of the above is/are correct?
NDA 2018 Paper 1
70
A committee of three has to be chosen from a group of 4 men and 5 women. If the selection is made at random, what is the probability that exactly two members are men?
NDA 2018 Paper 1
71
A bag contains 20 books out of which 5 are defective. If 3 of the books are selected at random and removed from the bag in succession without replacement, then what is the probability that all three books are defective?
NDA 2019 Paper 2
72
A coin is biased so that heads comes up thrice as likely as tails. For three independent tosses of a coin, what is the probability of getting at most two tails?
NDA 2019 Paper 2
73
If a coin is tossed till the first head appears, then what will be the sample space?
NDA 2019 Paper 2
74
The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. What are the number of boys and girls respectively in the class?
NDA 2019 Paper 2
75
If a fair die is rolled 4 times, then what is the probability that there are exactly 2 sixes ?
NDA 2019 Paper 2
76
Consider the following statements :
1. If A and B are mutually exclusive events, then it is possible that P(A) = P(B) = 0.6
2. If A and B are any two events such that P(A / B) = 1, then P($$\overline B $$ / $$\overline A $$) = 1.
Which of the above statement is/are correct?
1. If A and B are mutually exclusive events, then it is possible that P(A) = P(B) = 0.6
2. If A and B are any two events such that P(A / B) = 1, then P($$\overline B $$ / $$\overline A $$) = 1.
Which of the above statement is/are correct?
NDA 2019 Paper 2
77
There are 3 coins in a box. One is a two-headed coin; another is a fair coin; and third is biased coin that comes up heads 75% of time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?
NDA 2019 Paper 2
78
If 5 of a Company's 10 delivery trucks do not meet emission standards and 3 of them are chosen for inspection, then what is the probability that none of the trucks chosen will meet emission standards?
NDA 2019 Paper 2
79
Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on them is a prime number?
NDA 2019 Paper 2
80
From a deck of cards, cards are taken out with replacement. What is the probability that the fourteenth card taken out is an ace?
NDA 2019 Paper 1
81
IF A and B are two events such that P(A) = 0.5, P(B) = 0.6 and P(A $$\cap$$ B) = 0.4, then what is P($${\overline {A \cup B} }$$) equal to ?
NDA 2019 Paper 1
82
A problem is given to three students A, B and C whose probabilities of solving the problem are $${1 \over 2},{3 \over 4}$$ and $${1 \over 4}$$ respectively. What is the probability that the problem will be solved if they all solve the problem independently?
NDA 2019 Paper 1
83
A pair of fair dice is rolled. What is the probability that the second dice lands on a higher value than does the first?
NDA 2019 Paper 1
84
A fair coin is tossed and an unbiased dice is rolled together. What is the probability of getting a 2 or 4 or 6 along with head?
NDA 2019 Paper 1
85
If A, B and C are three events, then what is the probability that at least two of these events occur together?
NDA 2019 Paper 1
86
Two independent events A and B are such that P(A $$\cup$$ B) = $${2 \over 3}$$ and P(A $$\cap$$ B) = $${1 \over 6}$$. If P(B) < P(A), then what is P(B) equal to ?
NDA 2019 Paper 1
87
If two fair dice are rolled, then what is the conditional probability that the first dice lands on 6, given that the sum of numbers on the dice is 8 ?
NDA 2019 Paper 1
88
Two symmetric dice flipped with each dice having two sides painted red, two painted black, one painted yellow and the other painted white. What is the probability that both land on the same colour?
NDA 2019 Paper 1
89
There are n socks in a drawer, of which 3 socks are red. If 2 of the socks are chosen randomly and the probability that both selected socks are red is $${1 \over 2}$$, then what is the value of n ?
NDA 2019 Paper 1
90
Two cards are chosen at random from a deck of 52 playing cards. What is the probability that both of them have the same value ?
NDA 2019 Paper 1
91
In eight throws of a die, 5 or 6 is considered a success. The mean and standard deviation of total number of successes is respectively given by
NDA 2019 Paper 1
92
A and B are two events such that $$\overline A $$ and $$\overline B $$ are mutually exclusive. If P(A) = 0.5 and P(B) = 0.6, then what is the value of P(A / B) ?
NDA 2019 Paper 1
93
What is the probability that an interior point in a circle is closer to the centre than to the circumference ?
NDA 2019 Paper 1
94
If A and B are two events, then what is the probability of occurrence of either event A or event B ?
NDA 2019 Paper 1
95
Three distinct natural numbers chosen at random from 1 to 10. What is the probability that they are consecutive?
NDA Mathematics 1st September 2024
96
A, B, C are three mutually exclusive and exhaustive events associated with a random experiment. If 3P(B) = 4P(A) and 3P(C) = 2P(B), then what is P(A) equal to?
NDA Mathematics 1st September 2024
97
A die has two faces with number 4, three faces with number 5 and one face with number 6. If the die is rolled once, then what is the probability of getting 4 or 5?
NDA Mathematics 1st September 2024
98
A box contains 2 black, 4 yellow and 6 white balls. Three balls are drawn in succession with replacement. What is the probability that all three are of the same colour?
NDA Mathematics 1st September 2024
99
A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C may hit but B may lose?
NDA Mathematics 1st September 2024
100
A natural number x is chosen at random from the first 100 natural numbers. What is the probability that x2 + x > 50?
NDA Mathematics 1st September 2024
101
A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?
NDA Mathematics 1st September 2024
102
Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
NDA Mathematics 1st September 2024
103
For two events A and B, P(A) = P(A|B) = 0.25 and P(BIA) = 0.5. Which of the following are correct?
I. A and B are independent.
II. P(Ac ∪ Bc) = 0.875
III. P(Ac ∩ Bc) = 0.375
Select the answer using the code given below.
NDA Mathematics 1st September 2024
104
Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
NDA Mathematics 1st September 2024
105
The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
NDA Mathematics 1st September 2024
106
Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
NDA Mathematics 1st September 2024
107
In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
NDA Mathematics 1st September 2024
108
A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?
NDA Mathematics 21 April 2024
109
If a random variable $(x)$ follows binomial distribution with mean 5 and variance 4 , and $5^{23} P(X=3)=\lambda 4^\lambda$, then what is the value of $\lambda$ ?
NDA Mathematics 21 April 2024
110
If the letters of the word 'TIRUPATI' are written down at random, then what is the probability that both Ts are always consecutive?
NDA Mathematics 21 April 2024
111
Let $m = 77^n$. The index $n$ is given a positive integral value at random. What is the probability that the value of $m$ will have $1$ in the units place?
NDA Mathematics 21 April 2024
112
Three different numbers are selected at random from the first 15 natural numbers. What is the probability that the product of two of the numbers is equal to third number?
NDA Mathematics 21 April 2024
113
What is the minimum value of $P(A) + P(B)$?
NDA Mathematics 21 April 2024
114
What is the maximum value of $P(A) + P(B)$?
NDA Mathematics 21 April 2024
115
What is the minimum value of $P(B \cap C)$?
NDA Mathematics 21 April 2024
116
What is the maximum value of $P(B \cap C)$?
NDA Mathematics 21 April 2024
117
What is the value of $n$?
NDA Mathematics 21 April 2024
118
What is the value of $p + q$?
NDA Mathematics 21 April 2024
119
Three dice are thrown. What is the probability of getting a sum which is a perfect square?
NDA Mathematics 3 September 2023
120
A, B, C and D are mutually exclusive and exhaustive events.
If 2P(A) = 3P(B) = 4P(C) = 5P(D), then what is 77P(A) equal to ?
NDA Mathematics 3 September 2023
121
Two distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?
NDA Mathematics 3 September 2023
122
Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ?
NDA Mathematics 3 September 2023
123
The probability that a person recovers from a disease is 0.8. What is the probability that exactly 2 persons out of 5 will recover from the disease?
NDA Mathematics 3 September 2023
124
Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty, otherwise it is 45%. If it is seen that the building has collapsed, then what is the probability that it is due to faulty design?
NDA Mathematics 3 September 2023
125
A fair coin is tossed 6 times. What is the probability of getting a result in the 6th toss which is different from those obtained in the first five tosses ?
NDA Mathematics 3 September 2023
126
In a class, there are n students including the students P and Q. What is the probability that P and Q sit together if seats are assigned randomly?
NDA Mathematics 3 September 2023
127
What is the probability that all three boys sit together?
NDA Mathematics 3 September 2023
128
What is the probability that boys and girls sit alternatively?
NDA Mathematics 3 September 2023
129
What is the probability that no two girls sit together?
NDA Mathematics 3 September 2023
130
What is the probability that P and Q take the two end positions?
NDA Mathematics 3 September 2023
131
What is the probability that Q and U sit together?
NDA Mathematics 3 September 2023
132
Let A and B be two independent events such that
P(A̅) = 0.7, P(B̅) = k, P(A ∪ B) = 0.8, what is the value of k ?
NDA Mathematics 16 April 2023
133
A biased coin with the probability of getting head equal to $\frac{1}{4}$ is tossed five times. What is the probability of getting tail in all the first four tosses followed by head ?
NDA Mathematics 16 April 2023
134
A coin is biased so that heads comes up thrice as likely as tails. In four independent tosses of the coin, what is probability of getting exactly three heads ?
NDA Mathematics 16 April 2023
135
Let X and Y be two random variables such that X + Y = 100. If X follows Binomial distribution with parameters n = 100 and p = $\frac{4}{5}$, what is the variance of Y?
NDA Mathematics 16 April 2023
136
One bag contains 3 white and 2 black balls, another bag contains 2 white and 3 black balls. Two balls are drawn from the first bag and put it into the second bag and then a ball is drawn from the second bag. What is the probability that it is white ?
NDA Mathematics 16 April 2023
137
Three dice are thrown. What is the probability that each face shows only multiples of 3 ?
NDA Mathematics 16 April 2023
138
What is the probability that the month of December has 5 Sundays ?
NDA Mathematics 16 April 2023
139
A natural number n is chosen from the first 50 natural numbers. What is the probability that $n+\frac{50}{n}<50 $ ?
NDA Mathematics 16 April 2023
140
What is the probability of getting a composite number in the list of natural numbers from 1 to 50?
NDA Mathematics 4 September 2022
141
If n > 7, then what is the probability that C(n, 7) is a multiple of 7?
NDA Mathematics 4 September 2022
142
Two numbers x and y are chosen at random from a set of the first 10 natural numbers. What is the probability that (x + y) is divisible by 4 ?
NDA Mathematics 4 September 2022
143
A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies x + $\frac{1}{\text{x}}$ > 2 ?
NDA Mathematics 4 September 2022
144
Three fair dice are tossed once. What is the probability that they show different numbers that are in AP?
NDA Mathematics 4 September 2022
145
If P(A) = 0.5, P(B) = 0.7 and P(A ∩ B) = 0.3, then what is the value of P(A' ∩ B') + P(A' ∩ B) + P(A ∩ B') ?
NDA Mathematics 4 September 2022
146
Five coins are tossed once. What is the probability of getting at most four tails ?
NDA Mathematics 4 September 2022
147
Three fair dice are thrown. What is the probability of getting a total greater than or equal to 15 ?
NDA Mathematics 4 September 2022
148
The probability that a person hits a target is 0.5. What is the probability of at least one hit in 4 shots ?
NDA Mathematics 4 September 2022
149
During war, one ship out of 5 was sunk on an average in making a certain voyage. What is the probability that exactly 3 out of 5 ships would arrive safely?
NDA Mathematics 4 September 2022
150
A card is drawn from a pack of 52 cards. A gambler bets that it is either a spade or an ace. The odds against his winning are
NDA Mathematics 4 September 2022
151
The completion of a construction job may be delayed due to strike. The probability of strike is 0.6. The probability that the construction job gets completed on time if there is no strike is 0.85 and the probability that the construction job gets completed on time if there is a strike is 0.35. What is the probability that the construction job will not be completed on time ?
NDA Mathematics 4 September 2022
152
Two digits out of 1, 2, 3, 4, 5 are chosen at random and multiplied together. What is the probability that the last digit in the product appears as 0?
NDA Mathematics 10 April 2022
153
What is $P (G \cap \overline T)$ equal to?
NDA Mathematics 10 April 2022
154
What is $P(G | \overline T) $ equal to?
NDA Mathematics 10 April 2022
155
What is $P(\overline T | \overline G)$ equal to?
NDA Mathematics 10 April 2022
156
What is the probability that exactly 3 out of 6 workers suffer from a disease?
NDA Mathematics 10 April 2022
157
What is the probability that no one out of 6 workers suffers from a disease?
NDA Mathematics 10 April 2022
158
What is the probability that at least one out of 6 workers suffer from a disease ?
NDA Mathematics 10 April 2022
159
Consider the following relations for two events E and F :
1. P(E ∩ F) ≥ P(E) + P(F) - 1
2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F)
3. P(E ∪ F) ≤ P(E) + P(F)
Which of the above relations is/are correct?
NDA Mathematics 14 November 2021
160
If P(A|B) < P(A), then which one of the following is correct?
NDA Mathematics 14 November 2021
161
A problem is given to three students A, B and C, whose probabilities of solving the problem independently are $\rm \frac{1}{2}$, $\rm \frac{3}{4}$ and p respectively. If the probability that the problem can be solved is $\rm \frac{29}{32}$, then what is the value of p?
NDA Mathematics 14 November 2021
162
In a cricket match, a batsman hits a six 8 times out of 60 balls he plays. What is the probability that on a ball played he does not hit a six?
NDA Mathematics 14 November 2021
163
3-digit numbers are formed using the digits 1, 3, 7 without repetition of digits. A number is randomly selected. What is the probability that the number is divisible by 3?
NDA Mathematics 14 November 2021
164
What is the probability that the roots of the equation x2 + x + n = 0 are real, where n ∈ ℕ and n < 4?
NDA Mathematics 14 November 2021
165
If A and B are two events such that P(not A) = $\rm \frac{7}{10}$, P(not B) = $\rm \frac{3}{10}$ and P(A|B) = $\rm \frac{3}{14}$, then what is P(B|A) equal to?
NDA Mathematics 14 November 2021
166
Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?
NDA Mathematics 14 November 2021
167
Let two events A and B be such that P(A) = L and P(B) = M. Which one of the following is correct?
NDA Mathematics 18 April 2021
168
If $\rm P(A\cup B)=\dfrac{5}{6}, P(A\cap B)=\dfrac{1}{3}\:and\:P(\bar A)=\dfrac{1}{2}$, then which of the following is/are correct?
1. A and B are independent events.
2. A and B are mutually exclusive events.
Select the correct answer using the code given below.
NDA Mathematics 18 April 2021
169
A coin is tossed twice. If E and F denote occurrence of head on first toss and second toss respectively, then what is P(E ∪ F) equal to?
NDA Mathematics 18 April 2021
170
In a binomial distribution, the mean is $\dfrac{2}{3}$ and variance is $\dfrac{5}{9}$. What is the probability that random variable D = 2?
NDA Mathematics 18 April 2021
171
If A and B are two events such that $\rm P(A)=\dfrac{3}{4} \:and\: P(B)=\dfrac{5}{8}$, then consider the following statements:
1. The minimum value of P(A ∪ B) is $\dfrac{3}{4}.$
2. The maximum value of P(A ∩ B) is $\dfrac{5}{8}.$
Which of the above statements is/are correct?
NDA Mathematics 18 April 2021