Question

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.

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.