SOLUTION: Let A and B be events with P(A)=1/3, P(B)=1/4 and P(AUB)=1/2. Find the P(A ∩ B' ).

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Question 1124606: Let A and B be events with P(A)=1/3, P(B)=1/4 and P(AUB)=1/2. Find the P(A ∩ B' ).
Answer by ikleyn(52803) About Me  (Show Source):
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You may consider A and B as the subsets of the universal set U.



Then  (A ∩ B') = A \ (A ∩ B).       ( Elements of A that are not in B ) 

                                     The sign " \ " means subtraction of sets )


Therefore, you need first to find  P(A ∩ B)  and  then subtract it from P(A).



    Step 1.   P((A ∩ B) = P(A) + P(B) - P(AUB) = 1%2F3 + 1%2F4 - 1%2F2 = %284%2B3-6%29%2F12 = 1%2F12.


    Step 2.   P(A ∩ B') = P(A \ (A ∩ B)) = P(A) - P((A ∩ B) = 1%2F3 - 1%2F12 = 4%2F12 - 1%2F12 = 3%2F12 = 1%2F4.


Answer.  P(A ∩ B') = 1%2F4

Solved.