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# Suppose that A, B, and C are mutually independent events ISBN: 9780321923271 41

## Solution for problem 9E Chapter 1.4

Probability and Statistical Inference | 9th Edition

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Problem 9E

PROBLEM 9E

Suppose that A, B, and C are mutually independent events and that P(A) = 0.5, P(B) = 0.8, and P(C) = 0.9. Find the probabilities that (a) all three events occur, (b) exactly two of the three events occur, and (c) none of the events occurs.

Step-by-Step Solution:

Step 1 of 5:

Given that events A,B and C are mutually independent.

Also it is given that P(A)=0.5,P(B)=0.8 and P(C)=0.9.

Step 2 of 5:

(a)

Here we have to find the probability that all the three events occur.

Probability that all the three events occur is the probability of the event A B C.

Since the events are mutually independent, the probability of A B C is given by

P(A B C)=P(A)*P(B)*P(C)

=(0.5)*(0.8)*(0.9)

=0.36

Therefore, probability of all the three events occur is 0.36.

Step 3 of 5:

(b)

Here we have to find the probability that exactly two of the events occur.

Probability that exactly two of the three events occur is given by,

P(A B  )+P(A   C)+P(  B C)

where, , , denotes the non occurrence of the events A,B and C respectively.

We know that P(A)+P( )=1.

Therefore,

P( )=1-P(A)

=1-0.5

=0.5

P( )=1-P(B)

=1-0.8

=0.2

and

P( )=1-P(C)

=1-0.9

=0.1

Step 4 of 5

Step 5 of 5

##### ISBN: 9780321923271

This full solution covers the following key subjects: Events, occur, none, independent, mutually. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. The answer to “Suppose that A, B, and C are mutually independent events and that P(A) = 0.5, P(B) = 0.8, and P(C) = 0.9. Find the probabilities that (a) all three events occur, (b) exactly two of the three events occur, and (c) none of the events occurs.” is broken down into a number of easy to follow steps, and 46 words. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Since the solution to 9E from 1.4 chapter was answered, more than 253 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 9E from chapter: 1.4 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM.

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