Bag a contains 6 white and 7 black balls and another bag b contain 4 white and 5 black balls. A person drawing a ball from bag a and without noting its colour, it is put in the bag b. Now a ball is drawn from the bag b. Find the probability that the ball drawn is white
Answers
29/65 is the probability that the ball drawn is white
Step-by-step explanation:
Bag A - 6 White & 7 Black Balls - Total 13
Bag B - 4 White & 5 Black Balls - Total 9
Case 1 : Ball Drawn from Bag A is White
Probability = (6/13)
then Bag B has 5 White & 5 Black - total 10
Probability of White = 5/10 = 1/2
Total Probability of Case 1 = (6/13)(1/2) = 3/13
Case2 : Ball Drawn from Bag A is Black
Probability = (7/13)
then Bag B has 4 White & 6 Black - total 10
Probability of White = 4/10 =2/5
Total Probability of Case 2 = (7/13)(2/5) = 14/65
Total probability that the ball drawn is white = 3/13 + 14/65
= (15 + 14)/65
= 29/65
29/65 is the probability that the ball drawn is white
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