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

The Correct Option is B

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.