Let p(a)=.46 p(b\a)=.33 p(B\Ac)=.08

A. Find p(b)

B. Find p(a\b)

P(A) = 0.46

P(A^{c}) = 0.54

P(B| A) = 0.33

P (B | A^{c}) = 0.08

P(B) = P(A) P(B|A) + P(A^{c})P(B | A^{c}) = 0.46*0.33+0.54*0.08= 0.1518+0.0432= 0.1950

P (A^{c} | B) = P(A^{c}) P(B | A^{c}) /P(B) = 0.54*0.08/0.1950 = 0.0432/0.1950 =0.221538

Part B.....how do you find p(a\b)

P(A| B) = P(A) P(B|A) /P(B) = 0.46*0.33/0.1950 = 0.1518/0.1950 = 0.778462

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