Answer:
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
