Question

A bag contains 10 white balls and 3 red balls while another bag contains 3 white balls and 5 red balls. two balls are drawn at random from the first bag and put in the second bag and then a ball is drawn at random from the second bag. what is the probability that it is a white ball?

Answer 1

scenario (I) red ball drawn from bag 1 and then white from bag 2 
=3/8*2/7 
=6/56 

scenario(II) white ball from bag 1 and white from bag 2 
= 5/8*3/7 
=15/56 

Adding both = 21/56

Answer 2

probability = no of favourable outcome/ total no of outcomes
first bag = 2/13
second bag= 1/8
the no of white Ball in both bags are 13+8 = 21
13/21