A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is black and a king.

Given:

A card is drawn at random from a pack of 52 cards.

To do:

We have to find the probability that the card drawn is black and a king.

Solution:

A pack of cards contains 52 cards of four suits and two colours red and black.

Each suit has 1 to 13 numbers in which 4 are ace, jack, queen and king.

This implies,

The total number of possible outcomes $n=52$.

Number of cards which are black and a king $=2$

Total number of favourable outcomes $=2$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that the card drawn is black and a king $=\frac{2}{52}$

$=\frac{1}{26}$

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