Three groups $A, B, C$ are competing for positions on the Board of Directors of a company. The probabilities of their winning are $0.5, 0.3, 0.2$ respectively. If group $A$ wins,the probability of introducing a new product is $0.7$,and the corresponding probabilities for groups $B$ and $C$ are $0.6$ and $0.5$ respectively. The probability that the new product will be introduced is:

• A
  $0.18$
• B
  $0.35$
• C
  $0.10$
• D
  $0.63$