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

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Manager
Joined: 24 May 2016
Posts: 147
A box contains 10 apples. 9 of which are red. An apple is drawn...  [#permalink]

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19 Aug 2016, 09:16
8
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:22) correct 45% (02:18) wrong based on 100 sessions

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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

Intern
Joined: 29 Mar 2015
Posts: 11
Re: A box contains 10 apples. 9 of which are red. An apple is drawn...  [#permalink]

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19 Aug 2016, 23:32
5
When you choose (and then eat) the first apple, the probability of that apple being red is 9/10. So if we do the activity 1 times, the probability of it being red is 9/10.

For 2 times, it is (9/10)*(8/9)

For 3 times, it is (9/10)*(8/9)*(7/8)

You can notice that the numerator of the first term cancels with the denominator of the second. So we can see that the probability becomes 0.5 when the last term is 5/6 & it becomes less than 0.5 when the last term is 4/5.

9 accounts for n=1, so 4 will account for n=6, which is the answer.

Note that we cannot choose a "non red" apple in any of the steps because if we do, then the probability of the apple being a red apple equals to 1 always.

Hope it helps.
##### General Discussion
Manager
Joined: 15 Mar 2015
Posts: 111
Re: A box contains 10 apples. 9 of which are red. An apple is drawn...  [#permalink]

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19 Aug 2016, 09:38
1
When does 9/10*8/9*7/8*6/7.... become smaller than 0.5?

Might swell start with 3 as that is the first answer choice and you will still be able to add 1 every time.
(9*8*7)/(10*9*8)=514/720. Instead of calculating how many percent 514 is of 720 we can see that 514*2 is larger than 720 and thus the answer is >0.5 Not A.
(514*6)/(720*7)=3084/5140 Again 3084*2>6000>5140. Not B.
(3084*5)/(5140*6)=15420/30840 We are getting there, but this time 15420*2=30840 and thus =0.5 Which is not what we want. We can, however, deduce that multiplying the numerator with a smaller number than the denominator(as in (4*5)) would make 0.5 lower in the next answer choice. Therefore, the answer is not C, but D.

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

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18 Nov 2016, 07:36
EBITDA 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

probability that we got red first time is 9/10
probability we get red second time is 8/9
probability we get red third time is 7/8
probability we get red fourth time is 6/7
probability of getting red fith time is 5/6
if we multiply all these probabilities, we get 1/2 or 0.5. it must be true that from the next dawn, probability of getting red would be <0.5
therefore, the answer must be 6.
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Joined: 09 Sep 2013
Posts: 8748
Re: A box contains 10 apples. 9 of which are red. An apple is drawn...  [#permalink]

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21 Nov 2017, 15:07
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Re: A box contains 10 apples. 9 of which are red. An apple is drawn... &nbs [#permalink] 21 Nov 2017, 15:07
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# A box contains 10 apples. 9 of which are red. An apple is drawn...

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