SOLUTION: P(A)=7/20,P(A∪B)=191/400,P(A∩B)=49/400 ,P(B)=?

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Question 1181088: P(A)=7/20,P(A∪B)=191/400,P(A∩B)=49/400 ,P(B)=?
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
P(A)=7/20
P(A∪B)=191/400
P(A∩B)=49/400
P(B)=?
 P(A∪B)=P(A)+P(B)-P(A∩B)
191/400=7/20+P(B)-49/400
Multiply every term on both sides by 400
    191=140+400P(B)-49
    191=91+400P(B)
    100=400P(B)
100/400=P(B)
    1/4=P(B)

Edwin

Answer by ikleyn(52901) About Me  (Show Source):
You can put this solution on YOUR website!
.

Use the basic formula of Elementary Probability theory


    P(A U B) = P(A) + P(B) - P(A∩B).


Substitute the given values into the formula. You will get


    191%2F400 = 7%2F20 + P(B) - 49%2F400.


It implies


    P(B) = 191%2F400+-+7%2F20+%2B+49%2F400 = 191%2F400+-+140%2F400+%2B+49%2F400 = 100%2F400 = 1%2F4 = 0.25.    ANSWER

Solved, answered and carefully explained.

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