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Three groups A, Band Care contesting for positions on the Board of Directors of a company. The probabilities of their winning are 0.5, 0.3 and 0.2, respectively. If the group A wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for groups Band Care 0.6 and 0.5, respectively. Then, the probability that the new product will be introduced, is

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0.63

0.35

0.18

0.10

answer is A.

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Detailed Solution

Consider, the events $ε_{1}, ε_{2}, ε_{3}$ and A

A = introducing a new product

$\begin{array}{l} P (ε_{1}) = 0.5, P (ε_{2}) = 0.3, P (ε_{3}) = 0.2 \\ P (A / ε_{1}) = 0.7, P (A / ε_{2}) = 0.6, P (A / ε_{3}) = 0.5 \end{array}$

$∴$ Required probability

$\begin{array}{l} P (A) = P (ε_{1}) \times P (A / ε_{1}) + P (ε_{2}) \times P (A / ε_{2}) + P (ε_{s}) \times P (A / ε_{3}) \\ = 0.5 \times 0.7 + 0.3 \times 0.6 + 0.2 \times 0.5 \\ = 0.35 + 0.18 + 0.10 \\ = 0.63 \end{array}$

Hence, option (a) is correct.

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