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A box contains 10 apples, 9 of which are red. An apple is drawn from

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A box contains 10 apples, 9 of which are red. An apple is drawn from  [#permalink]

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New post 06 Nov 2019, 03:10
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Question Stats:

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A box contains 10 apples, 9 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7


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Re: A box contains 10 apples, 9 of which are red. An apple is drawn from  [#permalink]

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New post 06 Nov 2019, 04:15
Bunuel wrote:
A box contains 10 apples, 9 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7


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i used hit and trial to get value
9c6/10c6 = .4
n has to be 6
IMO D
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A box contains 10 apples, 9 of which are red. An apple is drawn from  [#permalink]

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New post 06 Nov 2019, 04:32
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I calculated valued when:

-> n=1 , p=9/10 . Total p=0.9
-> n=2 , p=8/9 . Total p=0.9*(8/9) it is greater than 0.5
-> n=3 , p=7/8 . Total p=0.9*(8/9)*(7/8) it is greater than 0.5
-> n=4 , p=6/7 . Total p=0.9*(8/9)*(7/8)*(6/7) it is greater than 0.5
-> n=5, p=5/6 . Total p=0.9*(8/9)*(7/8)*(6/7)*(5/6) it is greater than 0.5
-> n=6, p=4/5, total p = 0.9*(8/9)*(7/8)*(6/7)*(5/6) *(4/5) this is less than 0.5
for n>6, total p will continue to decrease
hence smallest possible value of n is 6

Answer: D
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A box contains 10 apples, 9 of which are red. An apple is drawn from   [#permalink] 06 Nov 2019, 04:32
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A box contains 10 apples, 9 of which are red. An apple is drawn from

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