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 group $B$ and $C$ are $0.6$ and $0.5$ respectively. The probability that the new product will be introduced is $0.09 \times k$ .The value of $k$ is

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Solution

Probability that a new project is announced $=$ probability that A wins and introduces project $+$ probability that B wins and introduces project $+$ probability that C wins and introduces project $= (0.5) (0.7) + (0.3) (0.6) + (0.2) (0.5) = 0.63 = 0.09 \times 7$
Hence, $k = 7$

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Similar questions

Q. 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

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

Q. 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 & C are 0.6 & 0.5 respectively. Find the probability that the new product will be introduced.
If ans can be expressed as

0.07 k

, then

k = ?

Two groups are competing for the position on the board of directors of a corporation. The probability that the first and the second groups will win are 0.6 and 0.4, respectively. Further, if the first group wins the probability of introducing a new product is 0.7 and the corresponding probability is 0.3, if the second group wins. Find the probability that the new product introduce was by the second group.

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Probability that a new project is announced=probability that A wins and introduces project + probability that B wins and introduces project + probability that C wins and introduces project=(0.5)(0.7)+(0.3)(0.6)+(0.2)(0.5)=0.63=0.09×7Hence,k=7

Probability that a new project is announced $=$ probability that A wins and introduces project $+$ probability that B wins and introduces project $+$ probability that C wins and introduces project $= (0.5) (0.7) + (0.3) (0.6) + (0.2) (0.5) = 0.63 = 0.09 \times 7$
Hence, $k = 7$