Question

Let A and B be two events with P(A) = 0.71 and P(B) = 0.44.

What is the largest possible value of P(A and B)?

What is the smallest possible value of P(A and B)?

Answer 1

We know that P(A or B) = P(A) + P(B) - P(A and B)

(a) To get the largest possible value of P(A and B), we will have to keep P(A or B) at the least.

We know that P(A and B) is always smaller than or equal to either P(A) or P(B) its Maximum possible value is Minimum [ P(A), P(B)] = MIN[ 0.71, 0.44].

Therefore Maximum of P(A and B) = 0.44

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If we want the maximum value of P(A or B) which can be 1, then P(A and B) has to be the minimum possible and ensure that P(A) + P(B) dont cross 1.

We see that P(A) + P(B) = 0.71 + 0.44 = 1.15 which exceeds 1 by 0.15.

Therefore Minimum Value of P(A and B) = 0.15