Chapter 12, Problem 18SGR

a.

To determine

The probability for the peter made the team and he is left handed.

Answer to Problem 18SGR

The probability is 0.5455.

Explanation of Solution

Given:

The table is given as:

  

Total person are:

  $22+15+6+5=48$

Evaluating the probability of left handed made team:

  $P\left(\text{left handed and made team}\right)=\frac{6}{48}$

Now, evaluating the probability that Peter made the team and he is left handed:

  $\begin{array}{l}P\left(\text{made team}|\text{left handed}\right)=\frac{P\left(\text{made team and left handed}\right)}{P\left(\text{left handed}\right)}\\ =\frac{\frac{6}{48}}{\frac{11}{48}}\\ =0.5455\end{array}$

Therefore, the probability is 0.5455.

b.

To determine

The probability for the Paul is right handed and he did not made the team.

Answer to Problem 18SGR

The probability is 0.8148.

Explanation of Solution

Given:

The table is given as:

  

Evaluating the probability that he did not made the team:

  $P\left(\text{did not make team}\right)=\frac{27}{48}$

Out of 48 persons, 22 are right handed and did not make team:

  $P\left(\text{right handed and did not make team}\right)=\frac{22}{48}$

The probability that Paul is right handed and he did not make the team:

  $\begin{array}{l}P\left(\text{right handed|did not make team}\right)=\frac{P\left(\text{right handed and did not make team}\right)}{P\left(\text{did not make team}\right)}\\ =\frac{\frac{22}{48}}{\frac{27}{48}}\\ =0.8148\end{array}$

Therefore, the probability is 0.8148.