Chapter 13, Problem 22SGR

To determine

If two cards are randomly chosen from a standard deck of cards with replacement then find the probability of successfully drawing in order, a three and then a queen.

Answer to Problem 22SGR

The probability of getting a 3 and then a queen is $\frac{1}{169}$ .

Explanation of Solution

Given information: It is given that from a deck of 52 cards 2 cards are drawn with replacement.

Calculation: Since the 2 cards are drawn with replacement therefore the total sample size will not change. Therefore the probability $P\left(3\text{ and }Q\right)$ of getting a 3 and then a queen is evaluated as,

  $\begin{array}{c}P\left(3\text{ and }Q\right)=\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)\\ =\left(\frac{1}{13}\right)\left(\frac{1}{13}\right)\\ =\frac{1}{169}\end{array}$

Hence the probability of getting a 3 and then a queen is $\frac{1}{169}$ .