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Assume that we have two events, A and B , that are mutually exclusive. Assume further that we know P ( A ) = .30 and P ( B ) = .40. a. What is P ( A ∩ B )? b. What is P ( A ∣ B )? c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer. d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 4.4, Problem 31E
Textbook Problem
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Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = .30 and P(B) = .40.

  1. a. What is P(AB)?
  2. b. What is P(AB)?
  3. c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer.
  4. d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

a.

To determine

Compute the value of P(AB).

Explanation of Solution

Calculation:

The two events A and B are mutually exclusive with probabilities P(A)=0.30 and P(B)=0.40.

Mutually Exclusive Events:

Two or more events are said to mutually exclusive if they have no element in common

b.

To determine

Compute the value of P(A|B).

c.

To determine

Check whether the statement is correct or not. And justify the answer.

d.

To determine

Explain what general conclusion you would make about mutually exclusive and independent events given the result of this problem.

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