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# Prove parts (b) and (c) of Theorem 1.4-1. ISBN: 9780321923271 41

## Solution for problem 4E Chapter 1.4

Probability and Statistical Inference | 9th Edition

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Problem 4E

PROBLEM 4E

Prove parts (b) and (c) of Theorem 1.4-1. Step-by-Step Solution:
Step 1 of 3

Solution 4E

Step1 of 3:

We have the events A and B are independent events.

We need to prove,

a).A1 and B are independent.

b).A1 and B1  are independent.

Step2 of 3:

a).

Let us assume that the events A and B are independent events

Consider,

P(A1 B) = P(A1/ B) P(B)                 [because P(A/ B) = ]

= [1 - P(A/B)] P(B)

= P(B) - P(A/B) P(B)

= P(B) - P(A B)                [because P(A/ B) = ]

= P(B) - [P(A) P(B)]         [because we know that A and B are independent]

= P(B)[1 - P(A)]

= P(B) P(A1).

Therefore, P(A1 B)...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321923271

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