Question

In a management trainee program 80% of trainees are female. 90% of the females attended university, and 78% of males attended university.

Q1 Are gender and attending university mutually exclusive? Can mutually exclusive events be independent? Explain.

Answer 1

Mutually exclusive events are those which cannot happen at the same time. Gender and attending University is not mutually exclusive as any person (male or female) can be attending University. Whether a male or female attends University does not affect the probability of female or male not attending university.

No, two mutually exclusive events cannot be independent. Suppose we toss a coin. It can show two outcomes head or tail but both cannot occur at the same time. This is an example of a mutually exclusive event. Independent events are those where the occurrence of one event does not affect the occurrence of the other. Here, if we get a head we cannot get a tail. So they are independent as the occurrence of any event is dependent on the other.