Question

Two cards are drawn simultaneously from the same set. The probability the at least one of them will be Ace of hearts is $\frac{k}{52}$. Find the value of $k$.

Answer 1

Let A= event the first card is an ace of hearts, and B= event that second card is an ace of hearts.

Since here both cannot be the ace of hearts so that here events A and B are mutually exclusive.

$\therefore P(A\cup B)=P\left(A\right)+P\left(B\right)$

and $P\left(A\right)=P\left(B\right)=\frac{1}{52}$ .

Hence $P(A\cup B)=\frac{1}{52}+\frac{1}{52}=\frac{2}{52}=\frac{1}{26}.$