Chapter 14, Problem 22E

a)

To determine

To find probability that neither has studied Calculus.

Answer to Problem 22E

The probability that neither has studied Calculus = 0.303

Explanation of Solution

Given:

P(Never) = 55% = 0.55

P(One) = 32% = 0.32

P(Two or more) = 0.13

P(no more than one) = 0.32

Formula:

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

  $\begin{array}{l}P\left(Neither\right)=P(Never)\times P(Never)\\ P\left(Neither\right)=0.55\times 0.55=0.303\end{array}$

Hence, probability that neither has studied Calculus is 30.3%

b)

To determine

To find probability that both have studied at least one semester of calculus.

Answer to Problem 22E

The probability that both have studied at least one semester of calculus = 0.203

Explanation of Solution

Given:

P(Never) = 55% = 0.55

P(One) = 32% = 0.32

P(Two or more) = 0.13

P(no more than one) = 0.32

P(Some) = 0.45

Formula:

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

  $\begin{array}{l}P\left(bothhavestudiedatleastone\right)=P(Some)\times P(Some)\\ P\left(bothhavestudiedatleastone\right)=0.45\times 0.45=0.203\end{array}$

Hence, probability that both have studied at least one semester of calculus is 20.3%

c)

To determine

To find probability that at least one has had more than one semester of calculus.

Answer to Problem 22E

The probability that at least one has had more than one semester of calculus= 0.697

Explanation of Solution

Given:

P(Never) = 55% = 0.55

P(One) = 32% = 0.32

P(Two or more) = 0.13

P(no more than one) = 0.32

P(Some) = 0.45

P(Neither) = 0.303

Formula:

Complement rule:

  $P(NotA)=1-P(A)$

  $\begin{array}{l}P\left(leastonehashadmorethanone\right)=1-P(Neither)\\ P\left(leastonehashadmorethanone\right)=1-0.303=0.697\end{array}$

Hence, probability that at least one has had more than one semester of calculus is 69.7%