Question

The bag 'a' contains 3 white and 2 black balls while the bag 'b' contains 2 white and 5 black balls.One of the bags is chosen at random and a ball is drawn from it.What is the probability that the first bag will contain 5 white ballsballs is white

Answer 1

Lets say bag 1 has 3 white balls and 2 black balls while bag 2 has 2 white balls and 5 black balls.    

P (bag1=white ball)= 3/5;  

P (bag1=black ball)=2/5;  

P (bag2=white ball)= 2/7;  

P (bag2=black ball)= 5/7;  

Now the condition of one white and one black ball is met if we get one from either of the bag and the other from the remaining bag.  

Case1:    

Lets say we get white ball from bag 1 and black from bag 2. Then the probability of that being true is  

3/5*5/7=3/7  

Case2:  

Lets say we get white ball from bag 2 and black from bag 1. Then the probability of that being true is  

2/7*2/5=4/35  

Since both the cases are possible, the probabilities will need to be added to arrive at the total probability.  

Thus 3/7+4/35=15/35=3/7