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# Tough and tricky 3: leap year

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Math Expert
Joined: 02 Sep 2009
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Tough and tricky 3: leap year [#permalink]

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11 Oct 2009, 17:25
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Question Stats:

58% (01:05) correct 42% (01:16) wrong based on 61 sessions

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Tough and tricky 3:

How many randomly assembled people are needed to have a better than 50% probability that at least 1 of them was born in a leap year?

A. 1
B. 2
C. 3
D. 4
E. 5
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Manager
Joined: 11 Sep 2009
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Re: Tough and tricky 3: leap year [#permalink]

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11 Oct 2009, 17:51
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Essentially, you need to find the number of people so that the probability of all of them not being from a leap year is LESS THAN 50%. The probability of any one person not being born on a leap year is approximately 3/4.

So you are essentially solving for:

$$(\frac{3}{4})^n < \frac{1}{2}$$

n = 1: 3/4 < 1/2? NO
n = 2: (3/4)(3/4) = 9 / 16 < 1/2? NO
n = 3 (3/4)(3/4)(3/4) = 27 / 64 < 1/2? YES

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Math Expert
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Re: Tough and tricky 3: leap year [#permalink]

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12 Oct 2009, 09:39
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Set of Tough & tricky questions is now combined in one thread: tough-tricky-set-of-problms-85211.html

You can continue discussions and see the solutions there.
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Re: Tough and tricky 3: leap year [#permalink]

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03 May 2011, 23:54
3 it is.Has to be an odd number of people. 1 and 2 are ruled out straightaway.
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Director
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Re: Tough and tricky 3: leap year [#permalink]

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14 May 2011, 10:18
why should there be an odd number of people ?
it is clear... if there is 1 person the probability is 1/4 ,
if there are 2 , the probability is 1/4 +1/4 = 0.5 or 50%.
if there are 3,
p(L) > 50%
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Re: Tough and tricky 3: leap year [#permalink]

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14 May 2011, 11:58
garimavyas wrote:
why should there be an odd number of people ?
it is clear... if there is 1 person the probability is 1/4 ,
if there are 2 , the probability is 1/4 +1/4 = 0.5 or 50%.
if there are 3,
p(L) > 50%

for two people - how can u add 1/4+1/4? may I know your logic
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Re: Tough and tricky 3: leap year [#permalink]

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30 Oct 2016, 10:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Tough and tricky 3: leap year   [#permalink] 30 Oct 2016, 10:39
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