Chapter 5, Problem 13PT

a.

To determine

To find: The probability that individual is getting cancer if he is a smoker.

Answer to Problem 13PT

The probability is 0.32

Explanation of Solution

Given:

The table is:

Event	Probability
Smokes	0.25
Smokes and get cancer	0.08
Does not smoke and does not get cancer	0.71

Calculation:

The probability that individual is getting cancer if he is a smoker is calculated as:

  $\begin{array}{c}P\left(\text{Cancer|Smoker}\right)=\frac{P\left(\text{Cancer and Smoker}\right)}{P\left(\text{Smoker}\right)}\\ =\frac{0.08}{0.25}\\ =0.32\end{array}$

Thus, the probability is 0.32.

b.

To determine

To find: The probability that individual gets cancer or is a smoker.

Answer to Problem 13PT

The probability is 0.29

Explanation of Solution

The probability that individual gets cancer or is a smoker is calculated as:

  $\begin{array}{c}P\left(\text{Smoker or Cancer}\right)=1-P\left(\text{Not cancer nor smoker}\right)\\ =1-0.71\\ =0.29\end{array}$

Thus, the probability is 0.29

c.

To determine

To find: The probability that at least once of the male gets cancer.

Answer to Problem 13PT

The probability is 0.2256

Explanation of Solution

The probability that at least once of the male gets cancer is calculated as:

  $\begin{array}{c}P\left(\text{Cancer}\right)=P\left(\text{Smoker or Cancer}\right)+P\left(\text{Smoker or Cancer}\right)-P\left(\text{Smoker}\right)\\ =0.29+0.08-0.14\\ =0.12\end{array}$

Now,

  $\begin{array}{c}P\left(\text{At least once gets cancer}\right)=1-P\left(2\text{}\text{ not cancer}\right)\\ =1-\left(0.88\right)\left(0.88\right)\\ =1-0.7744\\ =0.2256\end{array}$

Thus, the probability is 0.2256