   # Suppose that we have two events, A and B , with P ( A ) = .50, P ( B ) = .60, and P ( A ∩ B ) = .40. a. Find P ( A ∣ B ). b. Find P ( B ∣ A ). c. Are A and B independent? Why or why not? ### Essentials Of Statistics For Busin...

9th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9780357045435

#### Solutions

Chapter
Section ### Essentials Of Statistics For Busin...

9th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9780357045435
Chapter 4.4, Problem 30E
Textbook Problem
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## Suppose that we have two events, A and B, with P(A) = .50, P(B) = .60, and P(A ∩ B) = .40. a. Find P(A ∣ B). b. Find P(B ∣ A). c. Are A and B independent? Why or why not?

a.

To determine

Compute the value of P(A|B).

### Explanation of Solution

Calculation:

The probability values are P(A)=0.50,P(B)=0.60,and P(AB)=0.40.

The formula for conditional probability is given by:

P(A|B)=P(AB)P(B)

Here, P(B)=0

b.

To determine

Compute the value of P(B|A).

c.

To determine

Check whether the events A and B are independent or not.

Explain the reasons.

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