IIT-JEE 1995 Screening | Probability Question 87 | Mathematics

Let $$0 < P\left( A \right) < 1,0 < P\left( B \right) < 1$$ and
$$P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right) - P\left( A \right)P\left( B \right)$$ then

$$P\left( {B/A} \right) = P\left( B \right) - P\left( A \right)$$

$$P\left( {A' - B'} \right) = P\left( {A'} \right) - P\left( {B'} \right)$$

$$P\left( {A \cup B} \right)' = P\left( {A'} \right) - P\left( {B'} \right)$$

$$P\left( {A/B} \right) = P\left( A \right)$$

IIT-JEE 1993

MCQ (More than One Correct Answer)

-0.5

$$E$$ and $$F$$ are two independent events. The probability that both $$E$$ and $$F$$ happen is $$1/12$$ and the probability that neither $$E$$ nor $$F$$ happens is $$1/2.$$ Then,

$$\,P\left( E \right) = 1/3,P\left( F \right) = 1/4$$

$$\,P\left( E \right) = 1/2,P\left( F \right) = 1/6$$

$$\,P\left( E \right) = 1/6,P\left( F \right) = 1/2$$

$$\,P\left( E \right) = 1/4,P\left( F \right) = 1/3$$

IIT-JEE 1991

MCQ (More than One Correct Answer)

-0.5

For any two events $$A$$ and $$B$$ in a simple space

$$P\left( {A/B} \right) \ge {{P\left( A \right) + P\left( B \right) - 1} \over {P\left( B \right)}},P\left( B \right) \ne 0$$ is always true

$$P\left( {A \cap \overline B } \right) = P\left( A \right) - P\left( {A \cap B} \right)\,\,$$ does not hold

$$P\left( {A \cup B} \right) = 1 - P\left( {\overline A } \right)P\left( {\overline B } \right),$$ if $$A$$ and $$B$$ are independent

$$P\left( {A \cup B} \right) = 1 - P\left( {\overline A } \right)P\left( {\overline B } \right),$$ if $$A$$ and $$B$$ are disjoint.

IIT-JEE 1989

MCQ (More than One Correct Answer)

-0.5

If $$E$$ and $$F$$ are independent events such that $$0 < P\left( E \right) < 1$$ and $$0 < P\left( F \right) < 1,$$ then

$$E$$ and $$F$$ are mutually exclusive

$$E$$ and $${F^c}$$ (the complement of the event $$F$$) are independent

$${E^c}$$ and $${F^c}$$ are independent

$$P\left( {E|F} \right) + P\left( {{E^c}|F} \right) = 1.$$

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