A , B , C are three mutually exclusive and exhaustive events associated with a random experiment. If 3 P ( B )=4 P ( A ) and 3 P ( C )=2 P ( B ) , then what is P ( A ) equal to?

Step-by-step solution

Given that A , B , C are mutually exclusive and exhaustive events P ( ~A )+ P ( ~B )+ P ( C )=1 ....(i) Given 3 P ( B )=4 P ( A ) P ( A )= 3 4 P ( B ) ....(ii) and 3 P ( C )=2 P ( B ) P ( C )= 2 3 P ( B ) .....(iii) Put (ii) and (iii) in (i), we get aligned & 3 4 P(B)+P(B)+ 2 3 P(B)=1 & 9 P(B)+12 P(B)+8 P(B) 12 =1 & 29 P(B) 12 =1 P(B)= 12 29 aligned Put the value of P ( B ) in (ii), we get P ( ~A )= 3 4 P ( ~B )= 3 4 12 29 = 9 29