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Probability

by harsh.champ » Sun Feb 07, 2010 11:59 am
In a box containing 15 apples, exactly 6 apples are rotten. Each day one apple is taken out from the box. What is the probability that after four days there are exactly 8 apples in the box that are not rotten?

(A)12/91
(B)1/7
(C)2/13
(D)2/7
(E)None of the above

The correct answer is A.
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by shashank.ism » Sun Feb 07, 2010 12:06 pm
harsh.champ wrote:In a box containing 15 apples, exactly 6 apples are rotten. Each day one apple is taken out from the box. What is the probability that after four days there are exactly 8 apples in the box that are not rotten?

(A)12/91
(B)1/7
(C)2/13
(D)2/7
(E)None of the above

The correct answer is A.
Out of 15 6 apples are rotten and 9 are non rotten.
so in 4 days 3 rotten and 1 non rotten apple will be removed.

No ways to select 4 apples from 15 = 15C4 = 15*14*13*12/(4*3*2*1) = 15*13*7
No of ways to select 3 rotten apples from 6 = 6*5*4/(3*2*1) =20
No of ways to select 1 good apple from 9 = 9

Probability = 20*9/15*13*7 = 12/91


The correct answer is A.[/quote]
Last edited by shashank.ism on Sun Feb 07, 2010 2:24 pm, edited 1 time in total.
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by ajith » Sun Feb 07, 2010 12:12 pm
harsh.champ wrote:In a box containing 15 apples, exactly 6 apples are rotten. Each day one apple is taken out from the box. What is the probability that after four days there are exactly 8 apples in the box that are not rotten?

(A)12/91
(B)1/7
(C)2/13
(D)2/7
(E)None of the above

The correct answer is A.
Initially we have 9 apples not rotten and 6 rotten apples
in 4 days exactly 1 non-rotten apple and 3 rotten apples have to be removed

No ways to select 4 apples from 15 = 15C4 = 15*14*13*12/4*6 = 15*7*13
No of ways to select 3 rotten apples from 6 = 6*5*4/6 =20
No of ways to select 1 good apple from 9 = 9

Probability = 20*9/15*7*13 = 12/91
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