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 [tex]4C_2[/tex]
The number of ways of getting two kings is [tex]4C_2[/tex]
Total number of cases is [tex]52C_4[/tex]
The probability of getting two queens and two kings is given by
[tex]\text {probability}=\frac{\text {No.of fanourable cases}}{\text {Total no.of cases}}[/tex]
Substituting the values, we get;
[tex]probability=\frac{4C_2 \cdot 4C_2}{52C_4}[/tex]
Simplifying, we get;
[tex]probability=\frac{6 (6)}{270725}[/tex]
[tex]probability=\frac{36}{270725}[/tex]
[tex]probability=0.000133[/tex]
Thus, the probability of getting two queens and two kings is 0.000133
