Question

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is a black king.

Answer 1

Finding the probability that the card drawn is a black king:

Let $\text{P}\left(\text{E}\right)$ be the probability that the card drawn is a black king.

Total number of cards in a deck$=52$

$\therefore$The number of possible outcomes$=52$

The total number of black kings$=2$

$\therefore$The number of favourable outcomes$=2$

We know that $\text{P}\left(\text{E}\right)\text{=}\frac{\text{Number of favourable outcomes}}{\text{Number of possible outcomes}}$

So, $\text{P}\left(\text{E}\right)$$=\frac{2}{52}$

$=\frac{1}{26}$

Hence, the probability that the card drawn is a black king is $\frac{1}{26}$.