Chapter 13.4, Problem 8CFU

To determine

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

Answer to Problem 8CFU

Mutually inclusive, $\frac{20}{27}$

Explanation of Solution

Given:

The probability of selecting a boy or blonde haired person from $12$ girls, $5$ of whom have blonde hair and $15$ boys $6$ of whom have blonde hair.

Calculation:

The events are mutually inclusive since a boy can be blonde haired also.

Let A be the event of selecting a boy.

Let B be the event of selecting a blonde haired person

Total sample space $=12+15=27$

Therefore probability of event A is $P(A)=\frac{15}{27}$

And probability of event B is $P(B)=\frac{5+6}{27}=\frac{11}{27}$

And probability of selecting a boy with a blond hair $=\frac{6}{27}$

Hence,

  $\begin{array}{l}P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and B)}\\ P(A\text{ or }B)=\frac{15+11-6}{27}=\frac{20}{27}\end{array}$