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(A) Let $E_{1}$ and $E_{2}$ be the events that the first group and the second group win the competition,respectively.Let $A$ be the event of introduci

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$2$

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(A) Let $E_{1}$ and $E_{2}$ be the events that the first group and the second group win the competition,respectively.Let $A$ be the event of introducing a new product.Given:$P(E_{1}) = 0.6$$P(E_{2}) = 0.4$$P(A | E_{1}) = 0.7$$P(A | E_{2}) = 0.3$We need to find the probability that the new product was introduced by the second group,which is $P(E_{2} | A)$.By Bayes' theorem:$P(E_{2} | A) = \frac{P(E_{2}) P(A | E_{2})}{P(E_{1}) P(A | E_{1}) + P(E_{2}) P(A | E_{2})}$Substituting the values:$P(E_{2} | A) = \frac{0.4 	imes 0.3}{(0.6 	imes 0.7) + (0.4 	imes 0.3)}$$P(E_{2} | A) = \frac{0.12}{0.42 + 0.12}$$P(E_{2} | A) = \frac{0.12}{0.54}$$P(E_{2} | A) = \frac{12}{54} = \frac{2}{9}$

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