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A ball is randomly selected from a box containing white balls and blac
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19 Apr 2022, 01:48
19 Apr 2022, 01:48
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A ball is randomly selected from a box containing white balls and black balls only. There are 27 more white balls than black balls. If the probability of randomly selecting a white ball is 4/5, how many white balls must be added to the box so that the probability of randomly drawing a white ball is 7/8?
(A) 16
(B) 24
(C) 27
(D) 30
(E) 32
(A) 16
(B) 24
(C) 27
(D) 30
(E) 32
Re: A ball is randomly selected from a box containing white balls and blac
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19 Apr 2022, 19:21
19 Apr 2022, 19:21
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Quote:
A ball is randomly selected from a box containing white balls and black balls only. There are 27 more white balls than black balls. If the probability of randomly selecting a white ball is 4/5, how many white balls must be added to the box so that the probability of randomly drawing a white ball is 7/8?
Let number of white balls be W and number of black balls be B
There are 27 more white balls than black balls
W = B + 27
Total number of balls = W + B = B + 27 + B = 2B + 27
probability of randomly selecting a white ball = (B+27)/ 2B + 27 = 4/5
Solving it, B = 9, W= 36 and total number of balls = 36 + 9 = 45
Let x white balls must be added to the box so that the probability of randomly drawing a white ball is 7/8
Number of white balls be (36 + x)
Total number of balls = (45 + x)
probability of randomly drawing a white ball = (36 + x) / (45 + x) = 7/8
Solving it, x = 27
IMO C
gmatclubot
Re: A ball is randomly selected from a box containing white balls and blac [#permalink]
19 Apr 2022, 19:21
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