Chapter 5.2, Problem 43E

(a)

To determine

To find:

The probability of selected senator is a male Republican.

Answer to Problem 43E

$0.42$

Explanation of Solution

Given information:

The following table categorizes 100 senator individuals.

	Male	Female	Total
Democrat	36	16	52
Republican	42	4	46
Independent	2	0	2
Total	80	20	100

A senator is selected at random from this group.

Formula Used:

Probability of an event is given by

$\frac{\text{Number}\text{of}\text{Favorable}\text{Outcome}}{\text{Number}\text{of}\text{total}\text{outcome}}$

Calculation:

The number of male Republican senators is $42$.

Therefore,

$\begin{array}{c}P(\text{Male Republican})=\frac{42}{100}\\ =0.42\end{array}$

(b)

To determine

To find:

The probability of selected senator is a Democrat or a female.

Answer to Problem 43E

$0.56$

Explanation of Solution

Formula Used:

Probability of event A or B is given by

$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$

Calculation:

Number of Democrat is 52.

$P\left(D\right)=\frac{52}{100}$

Number of female is 20.

$P\left(F\right)=\frac{20}{100}$

Number of Democrat female is 16.

$P\left(D\cap F\right)=\frac{16}{100}$

The number of Democrat or a female senators is,

$\begin{array}{c}\\ P\left(D\cup F\right)=P\left(D\right)+P\left(F\right)-P\left(D\cap F\right)\\ P(\text{Democrat or Female})=\frac{52}{100}+\frac{20}{100}-\frac{16}{100}\\ =\frac{56}{100}\\ =0.56\end{array}$

(c)

To determine

To find:

The probability of selected senator is a Republican.

Answer to Problem 43E

$0.46$

Explanation of Solution

Calculation:

The number of Republican senatorsis,

$46$

Therefore,

$\begin{array}{c}P(\text{Republican})=\frac{46}{100}\\ =0.46\end{array}$

(d)

To determine

To find:

The probability of selected senator is not a Republican.

Answer to Problem 43E

$0.54$

Explanation of Solution

Calculation:

The number of Republican senators is 46.

For any event $A$, the rule of complements is defined as,

$P(A^c)=1-P(A)$

Therefore,

$\begin{array}{c}P(\text{Not Republican})=1-P(\text{Republican})\\ =1-\frac{46}{100}\\ =\frac{54}{100}\\ =0.54\end{array}$

(e)

To determine

To find:

The probability of selected senator is a Democrat.

Answer to Problem 43E

$0.52$

Explanation of Solution

Calculation:

The number of Democrat senators is $52$

Therefore,

$\begin{array}{c}P(\text{Democrat})=\frac{52}{100}\\ =0.52\end{array}$

(f)

To determine

To find:

The probability of selected senator is an Independent.

Answer to Problem 43E

$0.02$

Explanation of Solution

Calculation:

The number of Independent senators is,

$2+0=2$

Therefore,

$\begin{array}{c}P(\text{Independent}\text{})=\frac{2}{100}\\ =0.02\end{array}$

(g)

To determine

To find:

The probability of selected senator is a Democrat or an Independent.

Answer to Problem 43E

$0.54$

Explanation of Solution

Calculation:

Number of Democrat is 52.

$P\left(D\right)=\frac{52}{100}$

Number of Independent is 2.

$P\left(I\right)=\frac{2}{100}$

Number of Democrat Independent is 0.

$P\left(D\cap I\right)=\frac{0}{100}$

The number of Democrat or an Independent senators is

$\begin{array}{c}P\left(D\cup I\right)=P\left(D\right)+P\left(I\right)-P\left(D\cap I\right)\\ P(\text{Democrat or Independent})=\frac{52}{100}+\frac{2}{100}-0\\ =\frac{54}{100}\\ =0.54\end{array}$