Chapter 14, Problem 40E

a)

To determine

To find the probability that they reach all Christians.

Answer to Problem 40E

The probability that they reach all Christians = 0.1478

Explanation of Solution

Given:

  $\begin{array}{l}P(Christian)=62\%=0.62\\ P(Jewish)=12\%=0.12\\ P(Other)=16\%=0.16\end{array}$

Formula:

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

Using multiplication rule,

  $\begin{array}{l}P(4Christian)=P(Christian)\times P(Christian)\times P(Christian)\times P(Christian)\\ P(4Christian)=0.62\times 0.62\times 0.62\times 0.62\\ P(4Christian)=0.1478\end{array}$

Hence, probability that they reach all Christians is 0.1478.

b)

To determine

To find the probability that no Jews.

Answer to Problem 40E

The probability that no Jews = 0.5997

Explanation of Solution

Given:

  $\begin{array}{l}P(Christian)=62\%=0.62\\ P(Jewish)=12\%=0.12\\ P(Other)=16\%=0.16\end{array}$

Formula:

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

Complement rule,

  $\begin{array}{l}P(NotJewish)=1-P(Jewish)\\ P(NotJewish)=1-0.12=0.88\end{array}$

Using multiplication rule,

  $\begin{array}{l}P(3NotJewish)=P(NotJewish)\times P(NotJewish)\times P(NotJewish)\times P(NotJewish)\\ P(3NotJewish)=0.88\times 0.88\times 0.88\times 0.88\\ P(3NotJewish)=0.5997\end{array}$

Hence, probability that they reach all Christians is 0.1478.

c)

To determine

To find the probability that at least one person who is nonreligious.

Answer to Problem 40E

The probability that at least one person who is nonreligious=0.3439

Explanation of Solution

Given:

  $\begin{array}{l}P(Christian)=62\%=0.62\\ P(Jewish)=12\%=0.12\\ P(Other)=16\%=0.16\end{array}$

Formula:

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

Using addition rule,

  $\begin{array}{l}P(\mathrm{Re}ligous)=P(Christian)+P(Jewish)+P(Other)\\ P(\mathrm{Re}ligous)=0.61+0.12+0.16=0.90\end{array}$

Using multiplication rule,

  $\begin{array}{l}P(4\mathrm{Re}ligious)=P(\mathrm{Re}ligious)\times P(\mathrm{Re}ligious)\times P(\mathrm{Re}ligious)\times P(\mathrm{Re}ligious)\\ P(4\mathrm{Re}ligious)=0.90\times 0.90\times 0.90\times 0.90\\ P(4\mathrm{Re}ligious)=0.6561\end{array}$

Using complement rule,

  $\begin{array}{l}P\left(Atleastonenon-religious\right)=1-P(4\mathrm{Re}ligious)\\ P\left(Atleastonenon-religious\right)=1-0.6561=0.3439\end{array}$

Hence, probability that at least one person who is nonreligious = 0.3439