NDA 2018 Paper 1 | Probability Question 63 | Mathematics

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 and II

I and III

II and III

I, II and III

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

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 ?

0.6

0.7

0.8

0.9

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

Two fair dice are rolled. What is the probability of getting a sum of 7 ?

$${1 \over {36}}$$

$${1 \over {6}}$$

$${7 \over {12}}$$

$${5 \over {12}}$$

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

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?

P(A | B) < P(B | A) < P(A $$\cap$$ B)

P(A $$\cap$$ B) < P(B | A) < P(A | B)

P(B | A) < P(A | B) < P(A $$\cap$$ B)

P(A $$\cap$$ B) < P(A | B) < P(B | A)

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