Chapter 15, Problem 34E

(a)

To determine

To find: the kind of high school the student takes part in.

Explanation of Solution

Given:

  $\begin{array}{l}P\left(P\right)=0.70\\ P\left(G/P\right)=0.75\\ P\left(G/P\text{'}\right)=0.90\end{array}$

Formula used:

  $P\left(G\right)=P\left(G\cap P\text{'}\right)+P\left(G\cap P\right)$

Calculation:

Let P = Freshmen take part in school and public

Let G = Freshmen eventually graduate

  

  $\begin{array}{c}P\left(G\right)=P\left(G\cap P\text{'}\right)+P\left(G\cap P\right)\\ =0.27+0.525\\ =0.795\\ P\left(G|P\right)\ne P\left(G\right)\end{array}$

Therefore, freshmen’s possibility graduate may depend upon that kind of high school of the student took part in.

(b)

To determine

To find: the percent of freshmen eventually graduate.

Answer to Problem 34E

79.5%

Explanation of Solution

Given:

  $\begin{array}{l}P\left(P\right)=0.70\\ P\left(G/P\right)=0.75\\ P\left(G/P\text{'}\right)=0.90\end{array}$

Formula used:

  $P\left(G\right)=P\left(P\cap G\right)+P\left(P\text{'}\cap G\right)$

Calculation:

Let P = Freshmen take part in public and school

Let G = Freshmen eventually graduate

  

  $P\left(G\right)=P\left(P\cap G\right)+P\left(P\text{'}\cap G\right)$

using the tree diagram

  $\begin{array}{c}=0.525+0.7\\ =0.795\end{array}$

Approximately 79.5% of freshmen eventually graduate