Question

Three groups $A,B,C$ are contesting for position on the Board and Director 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 introduces, is

• A. $0.52$
• B. $0.63$
• C. $0.74$
• D. None of these

Answer 1

The correct option is B $0.63$

Given $P\left(A\right)=0.5,P\left(B\right)=0.3$ and $P\left(C\right)=0.2$
$\therefore P\left(A\right)+P\left(B\right)+P\left(C\right)=1$
So the events $A,B,C$ are exhaustive.
If $P\left(E\right)=$ probability of introducing a new product, then as given
$P\left(\frac{E}{A}\right)=0.7,P\left(\frac{E}{B}\right)=0.6$ and $P\left(\frac{E}{C}\right)=0.5$
$\therefore P\left(E\right)=P\left(A\right).P\left(\frac{E}{A}\right)+P\left(B\right).P\left(\frac{E}{B}\right)+P\left(C\right).P\left(\frac{E}{C}\right)$
$=0.5\times 0.7+0.3\times 0.6+0.2\times 0.5$
$=0.35+0.18+0.10=0.63$