Chapter 15, Problem 38E

(a)

To determine

To Explain: these statistics indication of lung condition and smoking are not independent.

Explanation of Solution

Statistics indication of lung condition and smoking are not independent. Smokers have greater chance of having the condition.

(b)

To determine

To find: the probability that an arbitrary chosen 60-year-old has this lung condition.

Answer to Problem 38E

0.2312

Explanation of Solution

Given:

  $\begin{array}{c}P\left(\text{Smoke}\right)=0.23\\ P\left(\text{Lung Condition | Smoke}\right)=0.57\\ P\left(\text{Lung Condition | Non-Smoke}\right)=0.13\end{array}$

Formula used:

  $P\left(\text{Lung Condition}\right)=\left[P\left(\text{Smoke}\right)\times P\left(\text{Lung Condition | Smoke}\right)\right]$

Calculation:

The probability is that a arbitrary chosen 60-year- old has lung condition is,

  $\begin{array}{c}P\left(\text{Lung Condition}\right)=\left[P\left(\text{Smoke}\right)\times P\left(\text{Lung Condition | Smoke}\right)\right]\\ +\left[P\left(\text{Non - Smoke}\right)\times P\left(\text{Lung Condition | Non-Smoke}\right)\right]\\ =\left[0.23\times 0.57\right]+\left[(1-0.23)\times 0.13\right]\\ =0.2312\end{array}$

The probability is that an arbitrary chosen 60- years- old has ling condition is 0.2312