P(A|B) = .1, P(B) = .7, P(A|B') = .5. Find P(B|A).

how do you do this?

Given : P( A | B ) = 0.1, P( A | B' ) = 0.5, P( B ) = 0.7 ........ (1)
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P( A | B ) = P( A ∩ B ) / P(B) = 0.1

∴ P( A ∩ B ) = (0.1) P(B) = (0.1)( 0.7 ) = 0.07

∴ P( A ∩ B ) = 0.07 ........................................… (2)
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P( A | B' ) = P( A ∩ B' ) / P(B') = 0.5

∴ P( A ∩ B' ) = (0.5) P(B')

∴ P(A) - P( A ∩ B ) = (0.5) (0.7)

∴ P(A) = 0.35 + 0.07 = 0.42 ................................... (3)
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From (2) and (3),

P( B | A ) = P( A ∩ B ) / P(A)

. . . . . . . . = (0.07) / (0.42)

. . . . . . . . = 1/6 ........................................… Ans.
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use formulae
P(A/B)= P(A INTERSETION B)/P(B)
SIMILARLY P(B/A)= P(A INTERSECTION B)/P(A)
AND P(A/B')= (P(A)-P(A INTERS B))/(1-P(B))

USE ALL THESE AND U GET ANSWERS R U SATISFIED WITH MY ANSWER