Question

If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting two queens and two kings.

Answer 1

Given:

If you are dealt 4 cards from a shuffled deck of 52 cards.

We need to determine the probability of getting two queens and two kings.

Probability of getting two queens and two kings:

The number of ways of getting two queens is $4C_2$

The number of ways of getting two kings is $4C_2$

Total number of cases is $52C_4$

The probability of getting two queens and two kings is given by

$\text {probability}=\frac{\text {No.of fanourable cases}}{\text {Total no.of cases}}$

Substituting the values, we get;

$probability=\frac{4C_2 \cdot 4C_2}{52C_4}$

Simplifying, we get;

$probability=\frac{6 (6)}{270725}$

$probability=\frac{36}{270725}$

$probability=0.000133$

Thus, the probability of getting two queens and two kings is 0.000133