Chapter 7.3, Problem 7.53E

(a)

To determine

To find: the $P\left(D|F\right)$ and means of this value

Answer to Problem 7.53E

0.6875

Explanation of Solution

Given:

	Male	Female
Democrat	40	11
Republicans	44	5

Calculation:

  $\begin{array}{c}P\left(D|F\right)=\frac{11}{11+5}\\ =\frac{11}{16}\\ =0.6875\end{array}$

There $P\left(D|F\right)$ is indicating that the probability of a female is democrat.

(b)

To determine

To find: $P\left(F|D\right)$ and means of this value.

Answer to Problem 7.53E

0.2157

Explanation of Solution

Given:

	Male	Female
Democrat	40	11
Republicans	44	5

Calculation:

  $\begin{array}{c}P\left(F|D\right)=\frac{11}{11+40}\\ =\frac{11}{51}\\ =0.2157\end{array}$

There $P\left(F|D\right)$ is indicating that the probability of a democrat is female.

(c)

To determine

To Explain: that events D and F mutually exclusive or not, justify answer.

Answer to Problem 7.53E

Not mutually exclusive.

Explanation of Solution

Given:

	Male	Female
Democrat	40	11
Republicans	44	5

Calculation:

  $\begin{array}{c}P\left(D\cap F\right)=\frac{11}{40+11+44+5}\\ =\frac{11}{100}\\ =0.11\end{array}$

There $P\left(D\cap F\right)=0.11$ this is not equal to zero which is indicating that the events are not mutually exclusive.

(d)

To determine

To Explain: that the events D and F independent or not, justify answer.

Answer to Problem 7.53E

Not independent.

Explanation of Solution

Given:

	Male	Female
Democrat	40	11
Republicans	44	5

Calculation:

  $\begin{array}{c}P\left(D\right)=\frac{40+11}{40+11+44+5}\\ =\frac{51}{100}\\ =0.51\\ P\left(F\right)=\frac{11+5}{40+11+44+5}\\ =\frac{16}{100}\\ =0.16\end{array}$

There $P\left(D\right)\ne P\left(D|F\right)andP\left(F\right)\ne P\left(F|D\right)$ it is indicating that the events D and F not independent.