Chapter 14, Problem 33E

a)

To determine

To explain the difference between disjoint and independent.

Explanation of Solution

Given:

If you draw one M&M, are the events of getting a red one and getting an orange one disjoint, inendependent or neither.

First, we need to understand about disjoint and independent events.

Disjoint events: The events that cannot occur at the same time.

Independent events: Occurrence of one event does not affect to the probability of the occurrence of another event.

For one draw, the probability of getting a red M&M and getting an orange M&M are disjoint events. Your single draw cannot both be red and orange.

b)

To determine

To explain the difference between disjoint and independent.

Explanation of Solution

Given:

If you draw two M&M's one after the other, are the events of getting a red on the first and a red on the second disjoint, independent, or neither?

First, we need to understand about disjoint and independent events.

Disjoint events: The events that cannot occur at the same time.

Independent events: Occurrence of one event does not affect to the probability of the occurrence of another event.

For two draws, the events of getting a red M&M on the first draw and a red M&M on the second draw are independent. Drawing a red on the first does not influence the probability of drawing a red on the second.

c)

To determine

To explain the difference between disjoint and independent.

Explanation of Solution

Given:

Can disjoint events ever be independent?

First, we need to understand about disjoint and independent events.

Disjoint events: The events that cannot occur at the same time.

Independent events: Occurrence of one event does not affect to the probability of the occurrence of another event.

Disjoint events can never be independent. Once you know that one of a pair of disjoint events has occurred, the other one cannot occur, so its probability has become zero.