prashant212 wrote:

Bunuel wrote:

The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq

B. q − pq

C. p + q − 2pq

D. p + q − pq

E. p + q

Probability of A occuring = p , Probability of A NOT occuring = 1-p

Probability of B occuring = q , Probability of B not occurring = 1-q

Probability of atleast of one of A and B occuring = 1-(1-p)(1-q) =

p+q -pq

DThis is not right. When you consider atleast one, it also means you are considering the possibility of both events occuring, which should be excluded as per the question.

So correct would be A occurs, B doesn't occur and B occurs, A doesn't occur = p(1-q) + q(1-p) = p+q-2pq