Chapter 10.4, Problem 18E

a.

To determine

Tocalculate:

The probability of the redbirds score and bluebirds do not score for given condition.

Answer to Problem 18E

The probability of the redbirds score and bluebirds do not score for the given condition is $0.1$ .

Explanation of Solution

Given information:

Condition: when the coach leaves the goalie in.

	Goalie	No Goalie
Redbirds score	$0.1$	$0.3$
Bluebird score	$0.1$	$0.6$

Calculation:

The probability of redbirds and bluebirds score, given the goalie and not goalie are stated in the table. It is required to find the probability that redbirds score and bluebirds do not score.

Assume, event $A$ denote Redbird score event $B$ denote goalie in. So, with the help of the given details,

  $\begin{array}{l}P\left(A\right)=0.5,P\left(\overline{A}\right)=0.5,P\left(B|A\right)=0.1,P\left(B|\overline{A}\right)=0.1\\ P\left(\overline{B}|A\right)=0.3,P\left(\overline{B}|\overline{A}\right)=0.6\end{array}$

It is required to get the redbird score and bluebird do not score when the goalie is in.

Therefore, required probability is as follows:

  $\begin{array}{l}P\left(redbirdscoreandbluebirddonotscore\right)\\ =\left(0.5\right)\left(0.1\right)+\left(0.5\right)\left(0.5\right)\\ =0.1\end{array}$

The answer is $0.1$ .

Hence, the probability of the redbirds score and bluebirds do not score is $0.1$

b.

To determine

To calculate:

The probability that redbirds score and bluebirds do not score for the give condition.

Answer to Problem 18E

the probability of the redbirds score and bluebirds do not score when the coach leaves the goalie out is $0.45$ .

Explanation of Solution

Given information:

Condition: when the coach leaves the goalie out.

	Goalie	No Goalie
Redbirds score	$0.1$	$0.3$
Bluebird score	$0.1$	$0.6$

Calculation:

The probability of redbirds and bluebirds score, given the goalie and no goalie are stated in the table.

It is required to find the probability that redbirds score and bluebirds do not score.

Assume, event $A$ denote redbird score event $B$ denote goalie in.

So, with the help of the given details:

  $\begin{array}{l}P\left(A\right)=0.5,P\left(\overline{A}\right)=0.5,P\left(B|A\right)=0.1,P\left(B|\overline{A}\right)=0.1\\ P\left(\overline{B}|A\right)=0.3,P\left(\overline{B}|\overline{A}\right)=0.6\end{array}$

It is required to get the redbird score and bluebird do not score when the goalie is out.

Therefore, required probability is as follows:

  $\begin{array}{l}P\left(redbirdscoreandbluebirddonotscore\right)\\ =\left(0.5\right)\left(0.3\right)+\left(0.5\right)\left(0.6\right)\\ =0.45\end{array}$

The answer is $0.45$ .

Hence, the probability of the redbirds score and bluebirds do not score when the coach leaves the goalie out is $0.45$ .

c.

To determine

To explain:

The coach’s decision based on part a and b.

Answer to Problem 18E

The coach’s decision based on part a and bis tokeep the goalie out.

Explanation of Solution

Given information:

Part a $=P\left(0.1\right)$

Part b $=P\left(0.45\right)$

	Goalie	No Goalie
Redbirds score	$0.1$	$0.3$
Bluebird score	$0.1$	$0.6$

Based on the probability $P\left(0.1\right)$ and $P\left(0.45\right)$ , coach should keep the goalie out.