Chapter 13, Problem 25SGR

To determine

From a deck of 52 cards find the probability of drawing a 10 or a diamond.

Answer to Problem 25SGR

The probability of drawing a 10 or a diamond is $\frac{4}{13}$ .

Explanation of Solution

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

Calculation: Since the card drawn is a 10 or a diamond which is the case of mutually exclusive events because this task can be done at the same time. Therefore probability $P\left(10\text{ or }D\right)$ of drawing a 10 or a diamond is evaluated as,

  $\begin{array}{c}P\left(10\text{ or }D\right)=P\left(10\right)+P\left(D\right)-P\left(10\text{ and }D\right)\\ =\frac{4}{52}+\frac{13}{52}-\frac{1}{52}\\ =\frac{16}{52}\\ =\frac{4}{13}\end{array}$

Hence the probability of drawing a 10 or a diamond is $\frac{4}{13}$ .