1.

Two groups are competing for the positions on the board ofddirectors of acorporation. The probabilities that the first and the secon groups win are 0.6 and 0.4 respectively. Further, if the first group wmS, the probability of introducing a new product is 0.7 and when the second group wins, the correspondmg probability is 0.3. Find the probablity that the new product introduced was by the second group.

Answer»

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Solution :Let `E_1`= event that the first group wins,
`E_2` = event that the SECOND group wins, and
E=event that a NEW product in INTRODUCED.
Then, `P(E_1)=0.6,P(E_2)=0.4`,
`P(E//E_1)=0.7,P(E//E_2)=0.3`
Required probability `=P(E_2//E)`
`=(P(E//E_2).P(E_2))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2))`


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