Math CentralQuandaries & Queries


Question from tom, a student:

Let A and B be events with p(A ∪ B)= 7/8, p(A ∩ B)= 1/4, p(A' )= 5/8
a. p(A)
b. p(B)
c. P(A ∩ B')
...problem for me is that if p(A') = 5/8 then P(A) should be 1/ that the p(A' ∪ A) = p(A ∪ B) = 7/8...however, the book says the answer for p(A) is 3/8...does that mean, my interpretation is wrong (because if it is, then all my answers would be crap)...or is it just another typographical error?

Hi Tom,

The event $A'$ is the complement of the event $A$ so $P(A) + P(A') = 1. $ But $P(A') = \large \frac58$ so $P(A) = \large \frac38.$


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