Chapter 13.3, Problem 70AYU

To determine

To find: The probability that a randomly selected faculty member is:

a. Female or under age 40.

Answer to Problem 70AYU

a. $P\left(femaleorunderage40\right)=\frac{7}{13}$.

Explanation of Solution

Given:

The faculty of the mathematics department at Joliet Junior College is composed of 4 females and 9 males.

Of the 4 females, 2 are under age 40, and of the 9 males, 3 are under age 40.

Formula Used:

$P\left(A{{\displaystyle \cup }}^{\text{}}B\right)=P\left(A\right)+P\left(B\right)-P\left(A{{\displaystyle \cap }}^{\text{}}B\right)$

Calculation:

Total number of faculties $=9+4=13$.

a. $Numberoffemale=4$.

$Numberoffacultyunderage40=2+3=5$.

$P\left(A{{\displaystyle \cup }}^{\text{}}B\right)=P\left(A\right)+P\left(B\right)-P\left(A{{\displaystyle \cap }}^{\text{}}B\right)$

$P\left(femaleorunderage40\right)=P\left(female\right)+P\left(underage40\right)-P\left(femaleandunderage40\right)$.

$P\left(femaleorunderage40\right)=\frac{4}{13}+\frac{5}{13}-\frac{2}{13}=\frac{7}{13}$.

$P\left(femaleorunderage40\right)=\frac{7}{13}$.

To determine

To find: The probability that a randomly selected faculty member is:

Answer to Problem 70AYU

b. $P\left(maleorfacultyoverage40 \right)=\frac{11}{13}$.

Explanation of Solution

Given:

The faculty of the mathematics department at Joliet Junior College is composed of 4 females and 9 males.

Of the 4 females, 2 are under age 40, and of the 9 males, 3 are under age 40.

Formula Used:

$P\left(A{{\displaystyle \cup }}^{\text{}}B\right)=P\left(A\right)+P\left(B\right)-P\left(A{{\displaystyle \cap }}^{\text{}}B\right)$

Calculation:

Total number of faculties $=9+4=13$.

b. $Numberofmales=9$.

$Numberoffacultyoverage40=2+6=8$.

$P\left(A{{\displaystyle \cup }}^{\text{}}B\right)=P\left(A\right)+P\left(B\right)-P\left(A{{\displaystyle \cap }}^{\text{}}B\right)$

$P\left(maleorfacultyoverage40 \right)=\frac{9}{13}+\frac{8}{13}-\frac{6}{13}=\frac{11}{13}$.

$P\left(maleorfacultyoverage40 \right)=\frac{11}{13}$.