it says there are 2 vacancies meaning the probabilities of them getting selected are mutually exclusive. so the answer is P(A!B)+P(!AB)=P(A)*P(!B)+ P(!A)*P(B)=(1/3*4/5)+(2/3*1/5)=2/5 P(!A) is the probability that A is not selected.

Way i did it: Probability of only one getting selected = P(Bill) OR P(Nina) BUT NOT BOTH. In terms of set this is: P(B OR N) = P(B) + P(N) - 2 * P(B AND N). Twice because i don't want them to be selected at the same time.

What is wrong with my calculation? I am thinking as follows: the answer is equal to 1/3 + 1/5 - P[A and B]. And I guess A and B are independent thus P[A and B] = 1/15. Then my answer is 7/15.

simple think like A.B' +A'B

Since Bill getting the job and Nina getting the job are not mutally exclusive, can we use addition rule?

P (Bill or Nina) = P(Bill) + P(Nina) - P(Bill and Nina) ? = 1/3 + 1/5 - (1/3 * 1/5) = 8/15 - 1/15 = 7/15 This is the wrong answer though!