Question

This question has two parts.

(A) A special roulette wheel, which has an equal number of red and black spots, has come up red four times in a row. Assuming the roulette wheel is fair, what concept allows a player to know that the probability of the next spin of the wheel will come up black is 0.5?

a. dependent events

b. mutually exclusive events

c. independent events

(B) In a survey, respondents were asked to indicate their favorite brand of cereal. They were only allowed one choice. What is the concept that implies it is not possible for a single respondent to state more than one brand as their favorite cereal?

a. independent events

b. dependent events

c. mutually exclusive events

Answer 1

A)

The correct option is,

c. independent events

We are given that their is an equal number of red and black spots. Also the wheel is fair. So,

The next spin of wheel is independent of the previous spin of wheel.

B)

The correct option is,

c. mutually exclusive events

Let their be two brands ( "brand A" and "brand B"). They are Mutually Exclusive if it is impossible for them to happen together:. Or P("Brand A" and "Brand B") = 0

Since a participant can choose one brand, the above condition is met and hence they are mutually exclusive events.