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Question

Two sets of candidates are competing for the positions on the board of directors of a company. The probabilities that first and second sets will win are 0.6 and 0.4 respectively. If the first set wins the probability of introducing a new product is 0.8 and the corresonding probability if the second set wins is 0.3. The probability that the new product will be introduced is 0.1k. Find the value of k.

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Solution

Let P(A1)= Probability that the first set wins =0.6 P(A2)= probability that the second set wins=0.4P(B)= probability that a new product is introduced P(B)=P(BA1)+P(BA2)=P(A1)P(BA1)+P(A2);P(BA2)...(1)
Now as per hypothesis P(BA1)=0.8,P(BA2)=0.3 Hence from (1),P(B)=06×08+04×03=0.60

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