Question
A bag has 4 red and 5 black balls, a second bag has 3 red and 7 black balls. One ball is drawn from the first and two from the second. Find the probability that out of three balls two are red and one is black.
Solution
In first bag. there are 4 red and 5 black balls and in second bag, there are 3 red and 7 black balls.
P(two red and one black ball) = P(‘one red ball from first bag and one red, one black from second bag’ or ‘one black ball from first bag and two red balls from second bag’ )
= P(one red ball from first bag and one red. one black from second bag) + P(one black ball from first bag and two red balls from second bag).
