Question

Three cards are drawn with replacement from a part of $52$ cards. Find the probability that the cards drawn are King, Queen, Jack.

Answer 1

There are $4$ king, $4$ queen and $4$ jack in the pack of $52$ cards.

Since the cards are drawn with replacement, then there will be $3!$ possibilities that these cards will occur together.

Also, the probability of occurrence of a king is,

$P\left(king\right)=\frac{4}{52}$

$=d\frac{1}{13}$

The probability of occurrence of a queen is,

$P\left(queen\right)=\frac{4}{52}$

$=\frac{1}{13}$

The probability of occurrence of a jack is,

$P\left(jack\right)=\frac{4}{52}$

$=\frac{1}{13}$

Therefore, the probability of occurrence of a king, a queen and a jack is,

$P=3!\times \frac{1}{13}\times \frac{1}{13}\times \frac{1}{13}$

$=6\times \frac{1}{2197}$

$=\frac{6}{2197}$