Given that P(A or B)= 1/4, P(A)=1/5, and P(A and B)= 1/8, find P(B). Express the probability as a simplified fraction.

Formula is

P( A or B) = P(A) + P(B) - P(A and B)

1/4 = 1/5 + P(B) - 1/8

Rearranging gives

P(B) =1/4 +1/8 - 1/5

Taking LCM (which is 40 here) and simplifying gives

P(B) = ( 10 + 5 - 8)/40 = 7/40

P(B) = 7/40 (which cannot be simplified further)

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