Chapter 13.3, Problem 42E

(a)

To determine

To find: The probability that a smoking-related death was the result of either cardiovascular disease or cancer.

Answer to Problem 42E

The probability that Carl can solve all $10$ problems on the test is $\frac{21}{1292}$ .

Explanation of Solution

Given:

The given Venn diagram is as follows.

  

Calculation:

The probability that a smoking related death was the result of either cardiovascular or cancer is as follows.

  $\begin{array}{c}P=\frac{\text{Number}\text{of}\text{Cardiovascular}\text{disease}+\text{Number}\text{of}\text{Respiratory}\text{disease}}{\text{Total}\text{number}\text{of}\text{}\text{death}}\\ =\frac{179,820+151,332}{418,890}\\ \approx 0.791\end{array}$

Therefore, the probability that a smoking-related death was the result of either cardiovascular disease or cancer is $0.791$ .

(b)

To determine

To find: The odds against a smoking-related death being caused by cancer.

Answer to Problem 42E

The odds against a smoking-related death being caused by cancer is $\frac{267,568}{151,322}$ .

Explanation of Solution

Given:

The given Venn diagram is as follows.

  

Calculation:

Let $A$ be the event for death being caused by cancer.

Determine the probability of success of event $A$ .

  $P=\frac{151,322}{418,890}$

Determine the probability of failure of event $A$ .

  $\begin{array}{c}P\text{'}=1-P\\ =1-\frac{151,322}{418,890}\\ =\frac{267,568}{418,890}\end{array}$

Find the odds against a smoking-related death being caused by cancer.

  $\begin{array}{c}\text{odds}=\frac{\frac{267,568}{418,890}}{\frac{151,322}{418,890}}\\ =\frac{267,568}{151,322}\end{array}$

Therefore, the odds against a smoking-related death being caused by cancer is $\frac{267,568}{151,322}$ .