Chapter 13.4, Problem 37E

To determine

To find probability of each event using a standard deck of cards.

Answer to Problem 37E

  $\frac{55}{221}$

Explanation of Solution

Given:

The P(both red or both queens)if $5$ cards are drawn without replacement.

Calculation:

The standard cards contains $26$ red cards and $4$ queens of which $2$ are red queens.

Sample space $52$

P (both red or both queens) $=$ P (both red) $+$ P (both queen) $-$ P (both red queens)

  $\begin{array}{l}=\frac{26}{52}\cdot \frac{25}{52}+\frac{4}{52}\cdot \frac{3}{52}-\frac{2}{52}\cdot \frac{1}{52}\\ =\frac{650}{2652}+\frac{12}{2652}-\frac{2}{2652}\\ =\frac{660}{2652}=\frac{55}{221}\end{array}$