Homework Sourse2 pA 6 pB A 3 pA u B 7 a pAB b pA B c pBC A d pBC S
2. p(A) = .6; p(B / A) = .3; p(A u B) = .7
a) p(AB) =
b) p(A / B) =
c) p(BC / A) =
d) p(BC) =
Solution
a) p(B / A) = .3
--> P(A and B)/P(A) = 0.3
So P(AB) = 0.3*0.6=0.18
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b) p(A u B) = .7
--> P(A)+P(B)- P(A and B)=0.7
--> 0.6+P(B)-0.18 = 0.7
SO P(B)= 0.7+0.18-0.6=0.28
p(A / B) = P(A and B)/P(B)
=0.18/0.28
=0.6428571
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c) p(BC / A) = P(A and B\')/P(A)
={P(A)-P(A and B)}/P(A)
=(0.6-0.18)/0.6
=0.7
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d) p(BC) = 1-P(B)=1-0.28= 0.72
