Question

Three groups A, B and C are contesting for position 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 position is 0.7 and the corresponding probabilities for group B and C are 0.6 and 0.5 respectively. The probability that a new position introduced is

• A. 0.52
• B. 0.63
• C. 0.74
• D. None of the above

Answer 1

Answer: (B)

0.63

Answer 2

To find the probability that a new position is introduced, you need to calculate the weighted average of the probabilities based on each group's probability of winning.
Let P(new position introduced) be the probability that a new position is introduced. Then, you can calculate it as follows:
P(new position introduced) = P(A wins)$\times$P(new position introduced by A)$+$P(B wins)$\times$P(new position introduced by B)$+$P(C wins)$\times$P(new position introduced by C)
P(new position introduced) = (0.5$\times$0.7)$+$(0.3$\times$0.6)$+$(0.2$\times$0.5)
P(new position introduced) = 0.35$+$0.18$+$0.1
P(new position introduced) = 0.63
So, the correct answer is (2) 0.63.