JEE Advanced Mathematics question
An event X can take place in conjunction with any one of the mutually exclusive and exhaustive events A, B and C. If A, B, C are equiprobable and the probability of X is , and the probability of X taking place when A has happened is while it is when B has taken place then the probability of X taking place in conjunction with C is
Answer: (A)
Solution
(equiprobable, exhaustive, mutually exclusive). Total probability theorem:
P(X)=P(A)P(X|A)+P(B)P(X|B)+P(C)P(X|C)
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