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 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 probability of X taking place on conjunction with C is

Engineering

Mathematics

Conditional Probability

Question

5/8

3/8

5/24

none of these

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Probability of A = Probability of B = Probability of C = $\frac{1}{3}$
Probability of X = $P (X) = \frac{5}{12} = P (A) x P (\frac{X}{A}) + P (B) x P (\frac{X}{B}) + P (C) x P (\frac{X}{C})$

Hence,

P (\frac{X}{C}) = \frac{5}{8}

Please subscribe our Youtube channel to unlock this solution.