Answer:
A) Both events are not independent.
B) Both events are not mutually exclusive
C) 8.33%
D) 80%
Step-by-step explanation:
A) Both events are not independent. This is because, If B occurs it means that it is very likely that J will occur as well.
B) Both events are not mutually exclusive. This is because it is possible for both events J and B to occur at the same time.
C) we want to find the probability that Joe who is not a business student will receive the job offer.
This is;
P(J|Not B) = P(J & Not B)/P(Not B)
Now,
P(J & Not B) = P(J) – (P(B) × P(J | B))
25% of the students who attended received job offers. Thus; P(J) = 0.25
40% were from the College of Business. Thus;
P(B) = 0.4
Among the business students, 50% received job offers. Thus;
P(J|B) = 0.5
Thus;
P(J & Not B) = 0.25 - (0.4 × 0.5)
P(J & Not B) = 0.25 - 0.2
P(J & Not B) = 0.05
Since P(B) = 0.4
Then, P(Not B) = 1 - 0.4 = 0.6
Thus;
P(J|Not B) = 0.05/0.6
P(J|Not B) = 0.0833 = 8.33%
D) This probability is represented by;
P(B | J) = P(B & J)/P(J)
P(B & J) = (P(B) × P(J | B)) = (0.4 × 0.5) = 0.2
P(B | J) = 0.2/0.25
P(B | J) = 0.8 = 80%
