Chapter 7, Problem 7.83RE

(a)

To determine

To Calculate: the probability that the person smokes.

Answer to Problem 7.83RE

  $\text{P}\left(\text{smoker}\right)=0.31$

Explanation of Solution

Given:

Smoke?
Gender	Yes	No	Total
Male	19	41	60
Female	12	28	40
Total	31	69	100

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ \text{P}\left(\text{smoker}\right)=\frac{31}{100}\\ =0.31\end{array}$

(b)

To determine

To Calculate: the probability that the person smokes if person is male.

Answer to Problem 7.83RE

  $\text{P}\left(\text{Male | smoker}\right)=0.6129$

Explanation of Solution

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Conditional Probability

  $P\left(A|B\right)=\frac{\text{P}\left(B\cap A\right)}{P\left(B\right)}$

Calculation:

  $\begin{array}{c}\text{P}\left(\text{Male smoker}\right)=\frac{19}{100}\\ =0.19\end{array}$

  $\begin{array}{c}\text{P}\left(\text{Male | smoker}\right)=\frac{\text{P}\left(\text{Male smoker}\right)}{\text{P}\left(\text{smoker}\right)}\\ =\frac{\raisebox{1ex}{$19$}\!\left/ \!\raisebox{-1ex}{$100$}\right.}{\raisebox{1ex}{$31$}\!\left/ \!\raisebox{-1ex}{$100$}\right.}\\ =\frac{19}{31}\\ =0.6129\end{array}$

(c)

To determine

To Explain: that the two events independent or not.

Answer to Problem 7.83RE

Not independent.

Explanation of Solution

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

  $\begin{array}{c}\text{P}\left(\text{Male}\right)=\frac{60}{100}\\ =0.60\end{array}$

It is observed that $\text{P}\left(\text{Male | smoker}\right)\ne \text{P}\left(\text{Male}\right)$ . It is indication that the events “smoker” and “Male” are not independent.