A bag contains 8 white and 6 black balls. A ball is drawn at random from the bag, its colour is observed and kept aside (ie, not returned in the bag). Three additional balls of the same colour as observed are put in the bag. If now two balls are drawn simultaneously at random from the bag, then the probability that these two balls are of different colours, is:
Answers
Given : A bag contains 8 white and 6 black balls.
A ball is drawn at random from the bag, its colour is observed and kept aside (ie, not returned in the bag).
Three additional balls of the same colour as observed are put in the bag.
now two balls are drawn simultaneously at random from the bag,
To Find : the probability that these two balls are of different colours
7/25
2/5
18/35
4/15
Solution:
White = 8
Black = 6
Total = 14
case 1 : White taken out probability = 8/14 = 4/7
Now white = 8 - 1 + 3 = 10
Black = 6
Total = 16
WB + BW
= (10/16)(6/15) + (6/16)(10/15)
= 120/240
= 1/2
Probability = (4/7) (1/2) = 2/7
case 2 : black taken out probability = 6/14 = 3/7
Now black = 6 - 1 + 3 = 8
White = 8
Total = 16
WB + BW
= (8/16)(8/15) + (8/16)(8/15)
= 128/240
= 8/15
Probability = (3/7) (8/15) = 8/35
2/7 + 8/35
= (10 + 8)/35
= 18/35
18/35 is the probability
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