Chapter 14, Problem 37E

a)

To determine

To find the probability that she goes three consecutive frames without a strike.

Answer to Problem 37E

The probability that she goes three consecutive frames without a strike = 0.027

Explanation of Solution

Given:

  $P\left(Strike\right)=70\%=0.70$

Formula:

  $Probability=\frac{Numberoffavorableoutcomes}{Totalpossibleoutcomes}$

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

Using complement rule,

  $\begin{array}{l}P(noStrike)=1-P(Strike)\\ P(noStrike)=1-0.7=0.30\end{array}$

Using multiplication rule,

  $\begin{array}{l}P(3nostrikes)=0.30\times 0.30\times 0.30\\ P(3nostrikes)=0.027\end{array}$

Hence, probability that she goes three consecutive frames without a strike is 0.027

b)

To determine

To find the probability that she make her first strike in third frame.

Answer to Problem 37E

The probability that she make her first strike in third frame = 0.063

Explanation of Solution

Given:

  $P\left(Strike\right)=70\%=0.70$

Formula:

  $Probability=\frac{Numberoffavorableoutcomes}{Totalpossibleoutcomes}$

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

Using complement rule,

  $\begin{array}{l}P(noStrike)=1-P(Strike)\\ P(noStrike)=1-0.7=0.30\end{array}$

Using multiplication rule,

  $\begin{array}{l}P(firststrikeinthirdframe)=0.30\times 0.30\times 0.70\\ P(firststrikeinthirdframe)=0.063\end{array}$

Hence, probability that she make her first strike in third frame is 0.063

c)

To determine

To find the probability that she has at least one strike in first three frames.

Answer to Problem 37E

The probability that she has at least one strike in first three frames = 0.973

Explanation of Solution

Given:

  $P\left(Strike\right)=70\%=0.70$

Formula:

  $Probability=\frac{Numberoffavorableoutcomes}{Totalpossibleoutcomes}$

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

Using complement rule,

  $\begin{array}{l}P(atleastonestrike)=1-P(3nostrikes)\\ P(atleastonestrike)=1-0.027=0.973\end{array}$

Hence, probability that she has at least one strike in first three frames is 0.973

d)

To determine

To find the probability that she bowls a perfect game.

Answer to Problem 37E

The probability that she bowls a perfect game = 0.0138

Explanation of Solution

Given:

  $P\left(Strike\right)=70\%=0.70$

Formula:

  $Probability=\frac{Numberoffavorableoutcomes}{Totalpossibleoutcomes}$

Multiplication rule:

  $P(AandB)=P(A)\times P(B)$

Using complement rule,

  $\begin{array}{}$ P(bowlsperfectgame)=P{(strikes)}^{12}$$ P(bowlsperfectgame)={(0.70)}^{12}=0.0138$\end{array}$

Hence, probability that she bowls a perfect game is 0.0138