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5 May, 14:01

Given a sample space, and events A and B, where P (A) = 0.5 and P (B) = 0.5. Which of the following values for P (A and B) are not possible?

a. All are possible

b. 0.35

c. 0.5

d. 0

e. 0.25

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Answers (1)
  1. 5 May, 17:12
    0
    Option a, option b, option c, option d are not possible values for P (A ∩ B)

    Solution:

    Given A and B are independent events.

    P (A) = 0.5 and P (B) = 0.5

    To find which of the following values for P (A and B) are not possible.

    P (A and B) = P (A ∩ B)

    P (A ∩ B) = P (A) * P (B)

    = 0.5 * 0.5

    P (A ∩ B) = 0.25

    Option a: All are possible.

    All answers are not possible for two independent events.

    Option b: 0.35

    We found that P (A and B) is 0.25.

    So, 0.35 is not possible value.

    Option c: 0.5

    We found that P (A and B) is 0.25.

    So, 0.5 is not possible value.

    Option d: 0

    We found that P (A and B) is 0.25.

    So, 0 is not possible value.

    Option e: 0.25

    We found that P (A and B) is 0.25.

    So, 0.25 is the possible value.

    Hence, 0.35, 0.5, 0 are not possible values.
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