Question

Three cards are drawn with replacement from a well shuffled pack of 52 cards. Find the probability that the cards are a king, a queen and a jack.

Answer 1

$$\begin{gathered} P\left(\text{king}\right)=P\left(A\right)=\frac{4}{52} \\ P\left(\text{queen}\right)=P\left(B\right)=\frac{4}{52} \\ P\left(\text{jack}\right)=P\left(C\right)=\frac{4}{52} \\ P\left(\text{king, queen and jack}\right)=3!\times P\left(A\right)\times P\left(B\right)\times P\left(C\right) \\ =3\times 2\times \frac{4}{52}\times \frac{4}{52}\times \frac{4}{52} \\ =\frac{6}{2197} \end{gathered}$$