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.

Question

Mathematics

Makhi Cooper

19 August, 05:51

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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Answers (1)

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Gabriel Johns · Answer 1

Answer and explanation:

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

To find:

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

P (A) = 0.4

So, 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) Is it possible that P (A and B) = 0.3? Explain why or why not.

Yes, it is possible as P (A and B) = 0.3 < P (A) = 0.4

(c) Is it possible that P (A or B) = 0.5? Explain why or why not.

Its is possible that P (A or B) = 0.05,

As 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.

So, P (A or B) can be any value within the range 0.4 to 1.

(d) Is it possible that P (A or B) = 0.3? Explain why or why not.

P (A or B) cannot be 0.3 as the least value of P (A or B) is 0.4.