Chapter 13.4, Problem 7CFU

To determine

To find if each pair of events is mutually exclusive or mutually inclusive and find the probability.

Answer to Problem 7CFU

Mutually exclusive, $\frac{10}{13}$

Explanation of Solution

Given:

The probability of choosing a penny or dime from $4$ pennies, $3$ nickels and $6$ dimes.

Calculation:

The events are mutually exclusive since penny and dime can’t be selected at the same time.

Let A be the event of choosing a penny.

Let B be the event of choosing a dime.

Total sample space $=4+3+6=13$

Therefore probability of event A is $P(A)=\frac{4}{13}$

Therefore probability of event B is $P(B)=\frac{6}{13}$

Hence,

  $\begin{array}{l}P(A\text{ and }B)=P(A)+P(B)\\ P(A\text{ and }B)=\frac{4}{13}+\frac{6}{13}=\frac{10}{13}\end{array}$