Question

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

• A. 0.18
• B. 0.35
• C. 0.1
• D. 0.63

Answer 1

The correct option is D 0.63

Let E be the event that a new product is introduced.
Then P(A) = 0.5, P(B) = 0.3, P(C) = 0.2
and $P\left(\frac{E}{A}\right)=0.7,P\left(\frac{E}{B}\right)=0.6,P\left(\frac{E}{C}\right)=0.5$
$\because$ A, B and C are mutually exclusive and exhaustive events.
$P\left(E\right)=P\left(A\right).P\left(\frac{E}{A}\right)+P\left(B\right).P\left(\frac{E}{B}\right)+P\left(C\right).P\left(\frac{E}{C}\right)$
$=0.5\times 0.7+0.3\times 0.6+0.2\times 0.5$
$=0.35+0.18+0.10=\mathrm{0.63.}$