Question

Bag I contains 8 white and 7 black balls and bag II contains 5 white and 4 black balls. One ball is randomly transferred from bag I to bag II. Then a ball is drawn from bag II. Find the probability that the ball so drawn is white.

Answer 1

Give that bag I contains 8 white and 7 black balls and Bag II contain 5 white and 4 black balls. 

One ball from I bag randomly put in II bag. 

So the possibility is that ball taken out from bag I is white. 

Then probability that white ball is choosen from bag I = 8/15

Now total number of balls in bag II = 5 + 1 = 6

Probability that white ball is choosen from bag II = 6/10

When both events occurs together 

∴ Probability = 8/15 × 6/10 = 48/150

Another possibility is that ball is choosen from bag I is black. 

Then probability that black ball is choosen from bag = 7/15

Now number of black ball in bag II = 4 + 1 = 5 

∴ Probability that black ball is choosen = 5/10

Probability that both events happen together 

= 7/15 × 5/10 = 35/150

∵ Both events are mutually exclusive so only one event can happen. 

∴ Required probability = 48/150 + 35/120

= 83/150