Consider the Venn diagram below. Each of the dots outside the circle represents a homeowner who was questioned about road improvements in their neighborhood. In this survey, 5 homeowners were asked whether they supported a new walking trail or a new roundabout in their neighborhood.

 Consider the Venn diagram below. Each of the dots outside the circle represents a homeowner who was questioned about road improvements in their neighborhood. In this survey, 5 homeowners were asked whether they supported a new walking trail or a new roundabout in their neighborhood.

The homeowners are labeled with their names: Ben, Elizabeth, Jerome, Max, and Shelby.

The two events represented in the Venn diagram are:

Event A: The homeowner said they support a new walking trail.
Event B: The homeowner said they support a new roundabout.
Ben, Jerome, and Max state that they support the new walking trail, but not the roundabout. Elizabeth says she supports the new roundabout but not the walking trail. Shelby says she supports neither road improvement.

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 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 no outcomes. Thus, P(A and B)=0 and the events are mutually exclusive. 

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