Question

$A,B$ and $C$ are contesting the election for the post of secretary of a club which does not allow ladies to become members. The probabilities of $A,B$ and $C$ wining the election are $\frac{1}{3},\frac{2}{9}$ and $\frac{4}{9}$ respectively. The probabilities of introducing the clause of admitting lady members to the club by $A,B,$ and $C$ are $0.6,0.7$ and $0.5$ respectively. The probability that ladies will be taken as members in the club after the election is

• A. $\frac{26}{45}$
• B. $\frac{5}{9}$
• C. $\frac{19}{45}$
• D. none of these

Answer 1

The correct option is A $\frac{26}{45}$

Probability of ladies being included in the club =
(Probability that A wins*probability that he introduces women) + (Probability that B wins*probability that he introduces women) + (Probability that C wins*probability that he introduces women) =
$\frac{1}{3}\ast 0.6+\frac{2}{9}\ast 0.7+\frac{4}{9}\ast 0.5=\frac{26}{45}$