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A box contains 5 white balls and 8 black balls. A ball is removed from
[#permalink]
18 Oct 2021, 05:31
18 Oct 2021, 05:31
Expert Reply
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Question Stats:
50% (04:20) correct
50% (04:24) wrong based on 2 sessions
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A box contains 5 white balls and 8 black balls. A ball is removed from the box and replaced by two balls of the other color (for example, if a white ball is removed, then it is replaced by two black balls and vise-versa). After that, a second ball is drawn. What is the probability that the second ball is black?
A. 1/2
B. 38/91
C. 53/91
D. 8/13
E. 5/7
A. 1/2
B. 38/91
C. 53/91
D. 8/13
E. 5/7
Re: A box contains 5 white balls and 8 black balls. A ball is removed from
[#permalink]
18 Oct 2021, 05:54
18 Oct 2021, 05:54
There are 2 scenarios:
- First: draw a white then a black ball
+ Chance to draw a white ball: 5/13, then number of white balls is 4 and black balls is 10
+ Chance to draw a black ball: 10/14 = 5/7
=> The chance to draw the first ball is white and second ball is black: 5/13 x 5/7 = 25/91
- Second: draw a black then a black ball
+ Chance to draw a black ball: 8/13, then the number of white balls becomes 7 and black balls is 7
+ Chance ro draw a black ball: 7/14 = 1/2
=> The chance to draw the first ball is black and the second ball is also black: 8/13 x 1/2 = 4/13
=> The chance to draw the second ball is black: 25/91 + 4/13 = 53/91
Choice C
- First: draw a white then a black ball
+ Chance to draw a white ball: 5/13, then number of white balls is 4 and black balls is 10
+ Chance to draw a black ball: 10/14 = 5/7
=> The chance to draw the first ball is white and second ball is black: 5/13 x 5/7 = 25/91
- Second: draw a black then a black ball
+ Chance to draw a black ball: 8/13, then the number of white balls becomes 7 and black balls is 7
+ Chance ro draw a black ball: 7/14 = 1/2
=> The chance to draw the first ball is black and the second ball is also black: 8/13 x 1/2 = 4/13
=> The chance to draw the second ball is black: 25/91 + 4/13 = 53/91
Choice C
gmatclubot
Re: A box contains 5 white balls and 8 black balls. A ball is removed from [#permalink]
18 Oct 2021, 05:54
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