Question

Three groups $A,B,C$ are contesting 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 groups $B$ and $C$ are $0.6$ and $0.5$ respectively. The probability that the new product will be introduced is given by

• A. $0.36$
• B. $0.35$
• C. $0.63$
• D. $0.53$

Answer 1

Answer: (B)

$0.35$

$P\left(A\right)=0.5,P\left(B\right)=0.3,P\left(C\right)=0.2$

If $N$ is for introducing new product, then

$P\left(N|A\right)=0.7,P\left(N|B\right)=0.6,P\left(N|C\right)=0.5$

Therefore,

$P\left(N\right)=P\left(A\right)\times P\left(N|A\right)+P\left(B\right)\times P\left(N|B\right)+P\left(C\right)\times P\left(N|C\right)=0.5\times 0.7+0.3\times 0.6+0.2\times 0.5=0.63$