Question

Kiersten applies for admission to the University of Southern California (USC) and Florida State University (FSU). She estimates that she has a 60% chance of being admitted to USC, a 70% chance of being admitted to FSU, and a 35% chance of being admitted to both universities.

(a) What is the probability that she will be admitted to either USC or FSU?

(b) What is the probability that she will not be admitted to FSU?

Short answer

a) The probability of being admitted to either USC or FSU is $0.95$

b)The probability of not being admitted to FSU is$0.4$

Step-by-step solution

Step 1. Given information

The probability of being admitted to USC is $60\%=0.6$

The probability of being admitted to FSU is$70\%=0.7$

The probability of being admitted to both universities is: $35\%=0.35$

Part(a) Step 1. To find probability of being admitted to either USC or FSU.

Let, $P\left(A\right)$is the probability of being admitted to USC.

So, $P\left(A\right)=0.6$

$P\left(B\right)$is the probability of being admitted to FSU.

$P\left(B\right)=0.7$

Probability of being admitted to both universities is:

$P(A\cap B)=0.35$

So, probability of being admitted to either USC or FSU is:

$$\begin{gathered} P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B) \\ =0.6+0.7-0.35 \\ =1.3-0.35 \\ =0.95 \end{gathered}$$

Part(b) Step 1. The probability of not being admitted to FSU.

The probability of not being admitted to FSU is:

$$\begin{gathered} P\left(\overline{A}\right)=1-P\left(A\right) \\ =1-0.6 \\ =0.4 \end{gathered}$$