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.
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