Question

A survey of people on pizza preferences indicated that 55 percent preferred pepperoni only, 30 percent preferred mushroom only, and 15 percent preferred something other than pepperoni and mushroom. Suppose one person who was surveyed will be selected at random. Let P represent the event that the selected person preferred pepperoni, and let M represent the event that the selected person preferred mushroom. Are P and M mutually exclusive events for the people in this survey? (A) Yes, because the joint probability of P and M is greater than 0. B) Yes, because the joint probability of P and M is greater than 1. C)Yes, because the joint probability of P and M is equal to 0. D) No, because the joint probability of P and M is equal to 1. E) No, because the joint probability of P and M is equal to 0.

Answer 1

Answer:

C) Yes, because the joint probability of P and M is equal to 0.

Step-by-step explanation:

Given that, P represents the event that the selected person preferred pepperoni only.

And M represents the event that the selected person preferred mushroom only.

so, P and M are two mutually exclusive events because two events are mutually exclusive if they do not occur together.

Here, P and M cannot occur at same time.

so, the joint probability of P and M i.e) probability of both P and M to occur at same time is zero.