Two of the residents asked were men, and they are represented by red dots labeled M1,M2; The other two residents asked were women, and they are represented by blue dots labeled W1,W2; The two events represented in the Venn diagram are:

 Consider the Venn diagram below. Each of the dots outside the circle represents a city resident who is surveyed by the local paper.  In this experiment, 4 residents were asked about eating at a restaurant during the week.

Two of the residents asked were men, and they are represented by red dots labeled M1,M2;
The other two residents asked were women, and they are represented by blue dots labeled W1,W2;
The two events represented in the Venn diagram are:

Event A: The event that a resident eats out at a restaurant at least once a week.
Event B: The event that a resident eats fast food at least once a week.
Both men surveyed stated that they ate fast food at least once a week, but not at restaurants. One of the women, labeled W1, stated that she ate fast food and at a restaurant at least once a week. The other woman, W2, stated that she ate out at a restaurant at least once a week.

Place the dots in the appropriate event given the information above (you may not use all of the dots), then determine if the events are mutually exclusive.

 

A and B are not mutually exclusive. We say that two events are mutually exclusive if they share no outcomes, that is, P(A and B)=0. Here, A and B share an outcome: W1. Thus, P(A and B)≠0 and the events are not mutually exclusive. 

Thanks