Answer
(a) P(A|B)=56/59
(b) P(A'|B)=3/59
(c) P(A|B')=1/2
(d) P(B|A)=14/29
Work Step by Step
266 K 12 40
271 K 44 16
274 K 56 3
A={12, 40, 44, 16},
B={40, 16, 3},
AB={40, 16},
A'={56,3},
B'={12, 44, 56},
P{A|B}=P(AB)/P(B)=$\frac{40+16}{40+16+3}$=56/59,
P{A'|B}=1-p{A|B}=3/59 (P(A'|B)=P(A'B)/P(B)=$\frac{3}{40+16+3}$=3/59),
P(A|B')=P(AB')/P(B')=$\frac{12+44}{12+44+56}$=1/2,
P(B|A)=P(A|B)P(B)/P(A)=$\frac{\frac{56}{59}*59}{12+40+44+16}$=56/116=14/29 (P(B|A)=P(AB)/P(A)=$\frac{40+16}{12+40+44+16}$=56/116=14/29
