Consider the Venn diagram below. Each of the dots outside the circle represents a biologist questioned about their research interests. 10 biologists are questioned about their research interests. Six biologists are marine biologists, represented by red dots and labeled M1,M2,M3,M4,M5,M6. Four biologists are zoologists, represented by blue dots and labeled Z1,Z2,Z3 and Z4. The two events represented in the Venn diagram are:

 Consider the Venn diagram below. Each of the dots outside the circle represents a biologist questioned about their research interests. 10 biologists are questioned about their research interests.

Six biologists are marine biologists, represented by red dots and labeled M1,M2,M3,M4,M5,M6.
Four biologists are zoologists, represented by blue dots and labeled Z1,Z2,Z3 and Z4.
The two events represented in the Venn diagram are:

Event A: The biologist is interested in studying insects.
Event B: The biologist is interested in studying salmon habitats.
The biologists who say they are only interested in studying insects are Z1,Z2,Z3,M5 and M6. The biologists who say they are only interested in studying salmon habitats are M1,M2,M3 and M4. The biologist who said they were not interested in either topic is Z4.   

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.

 

Thanks