Two groups are competing for the positions of the board of Directors of a Corporation. The probabilities 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 introduced was by the second group.

Explanation

`P(E_{1})=` Probability of first group wins `=0.6`


`P(E_{2})=` Probability of second group wins `=0.4`


`P(A | E_{1})=` Probability of introducing a new product if the first group wins `=0.7`


`{P}({A} | {E}_{2})=` Probability of introducing a new product if the second group wins `=`


`0.3`


probability of introducing new product by the second group is


`P(E_{2} | A)`.


Applying Baye's theorem,

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