Problem: A and B are two independent random variables, each with a greater than 0% chance of occurring.
Quantity A: P(A or B)
Quantity B: P(A) + P(B)
The above question is on the Gregmat website under quant problems. The correct answer is B. However, the question prompt doesn’t say whether the events are mutually exclusive or not. In a scenario where they are mutually exclusive, won’t A=B? I marked the answer as D.
However, the question prompt doesn’t say whether the events are mutually exclusive or not.
They can’t be. Notice that mutual exclusion means that P(A ∩ B) = 0. However, given A and B are independent, this means that P(A ∩ B) = P(A) P(B). If these events were mutually exclusive, this means that P(A) P(B) = 0 → at least one of P(A) and P(B) is 0. But the question says that each of them have a greater than 0% chance of occurrence, which makes this case impossible.
Hence we can show that A and B cannot be mutually exclusive. If the “has to be greater than 0%” case wasn’t there, then the answer would be D.
Thank you!