Question

A bag contains 5 white and 4 black balls and another bag contains 7 white and 9 black balls. A ball is drawn from the first bag and two balls are drawn from the second bag. What is the probability of drawing one white and two black balls? 

Answer 1

Bag I	Bag II
4B	7W
5W	9B
Total balls in bag I = 9	Total balls in bag II = 16

Required probability = `(5/9) ((""^9C_2)/(""^16C_2)) + (4/9) (( ""^7 C_1 xx ""^9C_1)/(""^16C_2))`

= `(5)/(9) xx (9xx8)/(16xx15) + (4)/(9) xx (7xx9)/( 8xx 15)`

= `(1)/(6) + (7)/(30) = (5+7)/(30) = (12)/(30) = (2)/(5)`.