bag contains 4 red & 5 black balls. another contains 3 red & 6 black balls. one ball is drawn from first bag & two balls from second bag. find prob that out of these three balls one is red & two are black

Probability that out of the 3 balls, 2 are red and one is black would be equivalent to the sum of probability of drawing either a red ball from the first bag and then drawing a red and black ball from the second one and probability of drawing  a black ball from the first bag and then drawing 2 red balls from the second bag. 

 

So P(RRB)  = R(RB from first bag)*P(R from the second bag) + P(RR from the first bag) * P(B from the second bag)