Chapter 13, Problem 12CT

a.

To determine

The probability that she will be admitted to either USC or FSU.

Answer to Problem 12CT

The probability that she will be admitted to either USC or FSUis $0.95$ .

Explanation of Solution

Given:

Kiersten applies for admission to the University of Southern California (USC) and Florida State University (FSU).

Chance of being admitted to USC = 60%

Chance of being admitted to FSU = 70%

Chance of being admitted to both universities = 35%

Calculation:

The probability that she will be admitted to either USC or FSU is,

Let USC be A and FSU be B

Therefore,

  $\begin{array}{l}P(A\cup B)=P(A)+P(B)-P(A\cap B)\\ \Rightarrow P(A\cup B)=(0.6)+(0.7)-(0.35)\\ \Rightarrow P(A\cup B)=0.95\end{array}$

Hence,the probability that she will be admitted to either USC or FSUis $0.95$ .

b.

To determine

The probability that she will not be admitted to FSU.

Answer to Problem 12CT

The probability that she will not be admitted to FSUis $0.3$ .

Explanation of Solution

Given:

Kiersten applies for admission to the University of Southern California (USC) and Florida State University (FSU).

Chance of being admitted to USC = 60%

Chance of being admitted to FSU = 70%

Chance of being admitted to both universities = 35%

Calculation:

The probability that she will not be admitted to FSUis,

Let USC be A and FSU be B

Therefore,

  $\begin{array}{l}P(\overline{B})=1-P(B)\\ \Rightarrow P(\overline{B})=1-0.7\\ \Rightarrow P(\overline{B})=0.3\end{array}$

Hence,the probability that she will not be admitted to FSU is $0.3$ .