Question

In: Statistics and Probability

The probability of A is 0.7, the probability of B is 0.8. What are the possible...

The probability of A is 0.7, the probability of B is 0.8. What are the possible values for the probability of both A and B happening?

Solutions

Expert Solution

Let P(A) and P(B) are probabilities of A and B respectively.

P(A) = 0.7 and P(B) = 0.8

Probability of both A and B happening = P(A B) = P(A) + P(B) - P(A B)

=> P(A B) = 0.7 + 0.8 - P(A B)

=> P(A B) = 1.5 - P(A B)

The maximum value of P(A B) will be 1 (maximum value of probability)

The minimum value of P(A B) will be max(P(A), P(B)) (Since A U B is union of A and B and P(A B) A and P(A B) B)

The minimum value of P(A B) will be max(0.7, 0.8) = 0.8

So, the maximum value of P(A B) = 1.5 - 0.8 = 0.7

and the maximum value of P(A B) = 1.5 - 1 = 0.5

Hence the possible values for the probability of both A and B happening are between 0.5 and 0.7.

orchestra answered 2 years ago
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