If $P\,(A) = \frac{1}{4},\,\,P\,(B) = \frac{5}{8}$ and $P\,(A \cup B) = \frac{3}{4},$ then $P\,(A \cap B) = $

  • A

    $\frac{1}{8}$

  • B

    $0$

  • C

    $\frac{3}{4}$

  • D

    $1$

Similar Questions

Probability that a student will succeed in $IIT$ entrance test is $0.2$ and that he will succeed in Roorkee entrance test is $0.5$. If the probability that he will be successful at both the places is $0.3$, then the probability that he does not succeed at both the places is

 $\mathrm{A}$ die is thrown. If $\mathrm{E}$ is the event $'$ the number appearing is a multiple of $3'$ and $F$ be the event $'$ the number appearing is even $^{\prime}$ then find whether $E$ and $F$ are independent ?

$P(A \cup B) = P(A \cap B)$ if and only if the relation between $P(A)$ and $P(B)$ is

  • [IIT 1985]

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that One of them is black and other is red.

A fair coin and an unbiased die are tossed. Let $A$ be the event ' head appears on the coin' and $B$ be the event ' $3$ on the die'. Check whether $A$ and $B$ are independent events or not.