a study of college business majors included 1...
a study of college business majors included 150 sophomores and 200 juniors. the study showed that 80 sophomores and 150 juniors had summer internships. one person from the study is selected at random. what is the probability that the person is a sophomore given that the person had a summer internship?\na. $\frac{8}{23}$\nb. $\frac{3}{7}$\nc. $\frac{8}{15}$\nd. $\frac{23}{35}$
Answer
# Explanation:
## Step1: Define the events
Let $A$ be the event that the person is a sophomore, and $B$ be the event that the person had a summer - internship.
## Step2: Calculate the number of people in event $B$
The number of people with summer internships is $80 + 150=230$.
## Step3: Calculate the number of people in $A\cap B$
The number of sophomores with summer internships is $n(A\cap B)=80$.
## Step4: Use the formula for conditional probability
The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, $P(A|B)=\frac{n(A\cap B)}{n(B)}$. Substituting the values we found, $P(A|B)=\frac{80}{230}=\frac{8}{23}$.
# Answer:
A. $\frac{8}{23}$