Three groups A, B, C are competing for positi | vedclass

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(D) Let $E$ be the event that a new product is introduced.Given probabilities of winning for groups $A, B, C$ are $P(A) = 0.5, P(B) = 0.3, P(C) = 0.2$

Vedclass · Accepted Answer

$0.63$

Vedclass · Answer

(D) Let $E$ be the event that a new product is introduced.Given probabilities of winning for groups $A, B, C$ are $P(A) = 0.5, P(B) = 0.3, P(C) = 0.2$.The conditional probabilities of introducing a new product are $P(E|A) = 0.7, P(E|B) = 0.6, P(E|C) = 0.5$.Since $A, B, C$ form a partition of the sample space (mutually exclusive and exhaustive events),we use the Law of Total Probability:$P(E) = P(A) 	imes P(E|A) + P(B) 	imes P(E|B) + P(C) 	imes P(E|C)$$P(E) = (0.5 	imes 0.7) + (0.3 	imes 0.6) + (0.2 	imes 0.5)$$P(E) = 0.35 + 0.18 + 0.10 = 0.63$.Thus,the probability that the new product will be introduced is $0.63$.

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