Two cards are drawn at random and without replacement from a pack of $52$ playing cards. Finds the probability that both the cards are black.

There are $26$ black cards in a deck of $52$ cards.

Let $P(A)$ be the probability of getting a black card in the first draw.

$\therefore $ $P(A)=\frac{26}{52}=\frac{1}{2}$

Let $\mathrm{P}(\mathrm{B})$ be the probability of getting a black card on second draw. since the card is not replaced,

$\therefore $ $P(B)=\frac{25}{51}$

Thus, probability of getting both the cards black $=\frac{1}{2} \times \frac{25}{51}=\frac{25}{102}$

Let $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happens is $\frac{1}{{12}}$ and the probability that neither $E$ nor $F$ happens is $\frac{1}{2},$ then

- [IIT 1993]

Three athlete $A, B$ and $C$ participate in a race competetion. The probability of winning $A$ and $B$ is twice of winning $C$. Then the probability that the race win by $A$ or $B$, is

Suppose that $A, B, C$ are events such that $P\,(A) = P\,(B) = P\,(C) = \frac{1}{4},\,P\,(AB) = P\,(CB) = 0,\,P\,(AC) = \frac{1}{8},$ then $P\,(A + B) = $

If $A$ and $B$ are two events such that $P\left( {A \cup B} \right) = P\left( {A \cap B} \right)$, then the incorrect statement amongst the following statements is

- [JEE MAIN 2014]

Events $E$ and $F$ are such that $P ( $ not $E$ not $F )=0.25,$ State whether $E$ and $F$ are mutually exclusive.