Question

If a die is thrown and a card is selected at random from a deck of $52$ cards. The probability of getting an even number on the die and a black king card is

$\left(a\right)\frac{1}{13}\left(b\right)\frac{1}{26}\left(c\right)\frac{1}{52}\left(d\right)\frac{1}{39}$

Answer 1

Let $A$ be the event of getting even number on the die and event $B$ be the event of selecting a black king card.

Then, $P\left(A\right)=\frac{3}{6}=\frac{1}{2}$
$P\left(B\right)=\frac{2}{52}=\frac{1}{26}$
Since, $A$ and $B$ are independent events.
$\therefore P(A\cap B)=P\left(A\right)\times P\left(B\right)$
$=\frac{1}{2}\times \frac{1}{26}$
$=\frac{1}{52}$
Ans : $\left(c\right)$