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2015-03-24T16:11:34+05:30

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Informations from diagram are:
P(U) = 0.1
P(V) = 0.6
P(W) = 0.3

P(C|U) = 0.4
P(C'|U) = 0.6
P(C|V) = 0.2
P(C'|V) = 0.8
P(C|W) = 0.7
P(C'|W) = 0.3

P(C|U)= P(U ∩ C)/ P(U)
⇒ 0.4 = P(U ∩ C) / 0.1
⇒ P(U ∩ C) = 0.4 × 0.1 = 0.04
Similarly 
P(U ∩ C') = 0.6×0.1 = 0.06
P(V ∩ C) = 0.6× 0.2 = 0.12
P(V ∩ C') = 0.6 × 0.8 = 0.48
P(W ∩ C) = 0.3×0.7 = 0.21
P(W ∩ C') = 0.3×0.3 = 0.09

P(C) = P(U ∩ C) + P(V ∩ C) + P(W ∩ C) = 0.04 + 0.12 + 0.21 = 0.37
P(C') = P(U ∩ C') + P(V ∩ C') + P(W ∩ C') = 0.06+0.48+0.09 = 0.63 

17. P(U|C) = P(U ∩ C) / P(C) = 0.04 / 0.37 = 0.108
18. P(V|C') = P(V ∩ C') / P(C') = 0.48 / 0.63 = 0.762
19. P(W|C) = P(W ∩ C) / P(C) = 0.21 / 0.37 = 0.567
20. P(U|C') = P(U ∩ C') / P(C') = 0.06 / 0.63 = 0.095
21. P(V|C) = P(V ∩ C) / P(C) = 0.12 / 0.37 = 0.324
22. P(W|C') = P(W ∩ C') / P(C') = 0.09 / 0.63 = 0.143
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