An event `X`can take place in conjuction with any one of the mutually exclusive andexhaustive events `A ,Ba n dC`. If `A ,B ,C`are equiprobable and the probability of `X`is 5/12, and the probability of `X`taking place when `A`has happened is 3/8, while it is 1/4 when `B`has taken place, then the probabililty of `X`taking place in conjuction with `C`is`5//8`b. `3//8`c. `5//24`d. none of theseA. `5//8`B. `3//8`C. `5//24`D. None of these

An event `X`can take place in conjuction with any one of the mutually

1.	An event `X`can take place in conjuction with any one of the mutually exclusive andexhaustive events `A ,Ba n dC`. If `A ,B ,C`are equiprobable and the probability of `X`is 5/12, and the probability of `X`taking place when `A`has happened is 3/8, while it is 1/4 when `B`has taken place, then the probabililty of `X`taking place in conjuction with `C`is`5//8`b. `3//8`c. `5//24`d. none of theseA. `5//8`B. `3//8`C. `5//24`D. None of these
Answer» Correct Answer - A `P(A) =P(B)=P(C)and P(A)+P(B)+P(C) =1` `thereforeP(A)=P(B)=P(C)=1/3.` Also, `P(X)=5/12,P(X//A)=3/8,P(X//B)=1/4` We have, `P(X)=P(A)P(X//A)+P(B)P(X//B)+P(C) P(X//C)` `therefore5/12=1/3{(3)/(8)+(1)/(4)+P(X//C)}` `impliesP(X//C)=5/8`

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