50 POINTS IF YOU HELP ME 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? A. 8 23 3 B. C. 8 15 23 D. 35​

= 0.3478  

Step-by-step explanation:

Given:-

- The number of sophomore, S = 150

- The sophomore and had summer internship, x = 80

- The number of juniors, J = 200

- The junior and had summer internship, y = 150

Find:-

What is the probability that the person is a sophomore given that the person had a summer internship?

Solution:-

- The total sum of sophomore and junior students is N:

                        N = S + J

                        N = 150 + 200

                        N = 350 students.

- We will denote event A as random selection of sophomore from total.

- We will denote event B as random selection of student who had summer internship.

- We are to determine the conditional probability that a person selected is sophomore given that the person had a summer internship. That is the probability of event A given that event B has already occured.

- The conditional probability can be written as:

                       P ( A / B ) = P ( A & B ) / P ( B )

Where,

       P ( A & B ) : The probability the person is a sophomore and had a summer internship.

       P ( B ): The probability that the person selected had a summer internship.

                     P ( A & B ) = x / N

                                       = 80 / 350

                                       = 0.22857143

                    P ( B ) = ( x + y ) / N

                              = ( 80 + 150 ) / 350 = 230/350

                              = 0.65714286

Therefore the required probability is:

                    P ( A / B ) = 0.22857143 / 0.65714286

                                     = 0.3478  ... Answer