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.

Explanation: Joint probability is the possibility of two events occuring at the same time. However, when they can't, those events are mutually exclusive or disjoint.

Disjoint events has a probability of occuring at the same time of 0. Because of that, the probability of union between those two events is the sum of the probabilities of each happening:

P(A and B) = P(A) + P(B)

For this survey, there are no intersection between preferring mushroom or pepperoni, so the events are mutually exclusive with a joint probability of 0.

Answer 2

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

Explanation:

If M and P are two sample spaces of their respective events, such that ( A ∩ B ) = Ø [phi or the empty set represented by ‘Ø’ contains no element]. Then the probability of either A or B happening will be written as follows:

P ( M ∪ P) = P (M) + P ( P ) ; where the symbol ‘∪’ represents union or the word ‘or’. So the probability of occurrence of either A or B when A and B are mutually exclusive events is equal to the probability of occurrence of A plus the probability of occurrence of B.