21. Five mark exercise problem IX

If \(A\), \(B\), \(C\) are any three events such that the probability of \(B\) is twice as that of probability of \(A\) and probability of \(C\) is thrice as that of probability of \(A\) and if \(P(A \cap B) = \frac{1}{6}\), \(P(B \cap C) = \frac{1}{4}\), \(P(A \cap C) = \frac{1}{8}\), \(P(A \cup B \cup C) = \frac{9}{10}\), \(P(A \cap B \cap C) = \frac{1}{15}\), then find \(P(A)\), \(P(B)\) and \(P(C)\)?

 

Answer:

 

\(P(A) =\) $\frac{i}{i}$

 

\(P(B) =\) $\frac{i}{i}$

 

\(P(C) =\) $\frac{i}{i}$