   Chapter 14.2, Problem 24E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# A die is rolled, and the number showing is observed. Determine whether the events E and F are mutually exclusive. Then find the probability of the event E ∪ F .a) E: The number is greater than 3.F: the number is less than 5.b) E: The number is divisible by 3.F: the number is less than 3.

To determine

(a)

To find:

Whether the events E and F are mutually exclusive and the probability of the event EF

Explanation

Given:

A die is rolled.

Approach:

Formula for finding the probability is P(A)=n(A)n(S) ...(1).

Here P(A) denotes the probability of the event A, n(A) is the favourable outcome of A, n(S) is the total outcome.

The events A and B are said to be mutually exclusive if P(AB)=0.

The formula for the union of A and B is P(AB)=P(A)+P(B)P(AB) ...(2).

Calculation:

Let E be the event that the number is greater than 3 and F be the event that the number is less than 5.

EF is the event that the number greater than 3 and less than 5.

n(E)=3, n(F)=4, n(S)=6

n(EF)=1, n(S)=6

Substituting n(EF)=0, n(S)=6 in

To determine

(b)

To find:

Whether the events E and F are mutually exclusive and the probability of the event EF

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