Answer to Question #5020 in Statistics and Probability for Revika
P(X) = 0.25
P(Y) = 0.35
P(Z) = 0.40
P(D|X) = 0.05
P(D|Y) = 0.04
P(D|Z) = 0.02
Now let's use the Bayes' theorem to determine the probability that the match was played at X:
P(X|D) = P(D|X)P(X) / [P(D|X)P(X)+P(D|Y)P(Y)+P(D|Z)P(Z)] = 0.05*0.25 / (0.05*0.25 + 0.04*0.35 + 0.02*0.40) = 0.0125/0.0345 ≈ 0.362.
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