There are three urns A, B and C. A contains $4$ white balls and 5 blue balls. Urn B contains $4$ white balls and $3$ blue balls. Urn C contains $3$ white balls and $6$  blue balls. One ball is drawn from each of these urns. What is the probability that out of these three balls drawn, two are white and one is blue? 

A bag contains $4$ red and $4$ black balls, another bag contains $2$ red and $6$ black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag. 

A company launches a new product and estimated that a person who comes across its advertisement will buy the product with a probability of $0.7$, and who does not see the advertisement will buy the product with a probability of $0.3$. If undefined of the people come across the advertisement, then what is the probability that a person who buys the product had come across the advertisement?

Three bags contain balls as shown in the table below :

A bag is chosen at random and two balls are drawn from it. They happened to be white and red. What is the probability that they came from bag III?