Chapter 12.3, Problem 11PPS

(a)

To determine

To Find: The probability that a student is a member of a club given that he is male.

Answer to Problem 11PPS

The required probability is 0.390.

Explanation of Solution

Given:

Total number of persons,

  $156+312+242+108=818$

Total number of male,

  $156+242=398$

Total number of female,

  $312+108=420$

So the probability that person is a male,

  $P(\text{male})=\frac{398}{818}$

The probability that person is a female,

  $P(\text{female})=\frac{420}{818}$

Out of these 818 persons, 156 are male and is a member of club so

  $P(\text{male and memeber of club})=\frac{156}{818}$

So the probability that a student is a member of a club given that he is male is,

  $\begin{array}{l}P(\text{memeber of club}\mid \text{male})=\frac{P(\text{male and memeber of club})}{P(\text{male})}\\ \begin{array}{l}=\frac{156/818}{398/818}\hfill \\ =0.390\hfill \end{array}\end{array}$

Hence, required probability is 0.390.

(b)

To determine

To Find: The probability that a student is not member of a club given that she is female.

Answer to Problem 11PPS

The required probability is 0.2571.

Explanation of Solution

Out of these 818 persons, 108 are female and not a member of club so

  $P(\text{not a member of club and female})=\frac{108}{818}$

So the probability that a student is not a member of a club given that she is female is,

  $\begin{array}{l}P(\text{not a member of club}\mid \text{female})=\frac{P(\text{female and not a memeber of club})}{P(\text{female})}\\ \begin{array}{l}=\frac{108/818}{420/818}\hfill \\ =0.2571\hfill \end{array}\end{array}$

Hence, required probability is 0.2571.

(c)

To determine

To Find: The probability that a student is male and not member of a club.

Answer to Problem 11PPS

The required probability is 0.6914.

Explanation of Solution

Out of these 818 persons, 242 are not a member of club and male so

  $P(\text{not a member of club and male})=\frac{242}{818}$

Out of these 818 persons, 350 are not a member of club so

  $P(\text{not a member of club})=\frac{350}{818}$

So the probability that student is male, given that he is not a member of a club is,

  $\begin{array}{l}P(\text{male}\mid \text{not a member of club})=\frac{P(\text{not a member of club and male})}{P(\text{not a member of club})}\\ \begin{array}{l}=\frac{242/162}{350/162}\hfill \\ =0.6914\hfill \end{array}\end{array}$

Hence, required probability is 0.6914.