A, B and C are contesting in an election for the post of secretary of a club which does not allow ladies to become members. The probabilities of A, B and C winning the election are13,29 and 49respectively. 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

Let E be the event of introducing the clause of admitting lady members to the club. ThenP(E)=P(A)⋅PEA+P(B)⋅PEB+P(C)⋅PEC=13×0.6+29×0.7+49×0.5=1.8+1.4+2.09=5.29=5290=2645

A, B and C are contesting in an election for the post of secretary of a club which does not allow ladies to become members. The probabilities of A, B and C winning the election are13,29 and 49respectively. 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

Let E be the event of introducing the clause of admitting lady members to the club. ThenP(E)=P(A)⋅PEA+P(B)⋅PEB+P(C)⋅PEC=13×0.6+29×0.7+49×0.5=1.8+1.4+2.09=5.29=5290=2645

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A, B and C are contesting in an election for the post of secretary of a club which does not allow ladies to become members. The probabilities of A, B and C winning 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

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none of these

$\frac{26}{45}$

$\frac{5}{9}$

$\frac{19}{45}$

answer is A.

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Detailed Solution

Let E be the event of introducing the clause of admitting lady members to the club. Then
$\begin{array}{l} P (E) = P (A) \cdot P (\frac{E}{A}) + P (B) \cdot P (\frac{E}{B}) + P (C) \cdot P (\frac{E}{C}) \\ = [\frac{1}{3} \times 0 .6 + \frac{2}{9} \times 0 .7 + \frac{4}{9} \times 0 .5] \\ = [\frac{1 .8 + 1 .4 + 2 .0}{9}] = \frac{5 .2}{9} = \frac{52}{90} = \frac{26}{45} \end{array}$