Question

Suppose that P(A) = 0.4 and P(B) is unknown. (a) Is it possible that P(A and...

Suppose that P(A) = 0.4 and P(B) is unknown.

(a) Is it possible that P(A and B) = 0.5? Explain why or why not. (b) Is it possible that P(A and B) = 0.3? Explain why or why not. (c) Is it possible that P(A or B) = 0.5? Explain why or why not. (d) Is it possible that P(A or B) = 0.3? Explain why or why not.

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Homework Answers

Answer #1

P(A) = 0.4

a) P(A and B) cannot be 0.5 because maximum value of P(A and B) is the lowest of P(A) and P(B). The range of P(A and B) is 0 to 0.4. Therefore, P(A and B) cannot be greater than P(A).

b) It is possible. Here, P(A and B) = 0.3, which is less than P(A)

c) Its is possible that P(A or B) = 0.05, because P(A or B) can have a least value equal to highest of P(A) and P(B) and maximum value of P(A or B) is 1. In this case, P(A or B) can be any value within the range 0.4 to 1.

d) P(A or B) cannot be 0.3. The least value of P(A or B) is 0.4

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