Let W denote the event " winner is a women". Then W′ denote the event "winner is not a men".
Let M denote the event "winner is married". Then M′ denote the event "winner is not married".
P(W)=12065=2413
P(W′)=1−P(W)=1−2413=2411
P(W)=12065=2413
P(W′)=1−P(W)=1−2413=2411
P(M∣W)=6545=139
P(M∣W′)=120−6580−45=117 By Bayes' Theorem
P(W∣M)=P(M∣W)P(W)+P(M∣W′)P(W′)P(M∣W)P(W)
P(W∣M)=139(2413)+117(2411)139(2413)=169
If the winner is married, the probability that it is a woman is 169.
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