A bag contains 7 white and 9
black balls. Two balls are
randomly taken out from the
bag one by one. Find the probability of getting one white
ball and another a black ball?
Answers
Solution :
The bag originally contains 7 white balls and 9 black balls.
The total sample space is 16 balls.
From here, two balls are taken out without replacement.
We need to find the probability of getting one white and one black ball .
When the first ball is chosen out of the 16 balls :
The probability that it is a white ball :
> [ Number of white balls ]/[Total number of balls ]
> 7/16
Probability of getting a black ball :
> [ Number of black balls ]/[Total number of balls ]
> 9/16
Now, as the first ball isnt returned :
(a), If it was a white ball
Remaining number of balls : 15 ,
Number of remaining white balls is 6 and that of black balls is 9.
Probability of getting a white ball now is 6/15 and that of a black ball is 9/15.
(b) If it is a black ball :
Remaning number of balls : 15
Number of remaining white balls is 7 and that of black balls is 8
Probability of getting a white ball now is 7/15 and that of a black ball is 8/15.
This is the required answer,
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