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# ps-leap year

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ps-leap year [#permalink]  30 May 2005, 13:54
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How many randomly assembled ppl do u need to have a better than 50% prob. that at least 1 of them was born in a leap year ?
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Director
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Re: ps-leap year [#permalink]  30 May 2005, 14:14
christoph wrote:
How many randomly assembled ppl do u need to have a better than 50% prob. that at least 1 of them was born in a leap year ?

prob of being born in a leap year is 1/4 and not being born in a leap year is 3/4
(note: if considering days of birth, than probabilities will be slightly different because leap year has 366 days, so prob of being born on a leap year is 366/(3*365+366) = approx 1/4 )

prob(none out of n people is born in a leap year) is (3/4)^n

so

prob(at least one of them is born in a leap year) = 1-(3/4)^n >1/2 => (3/4)^n < 1/2

minimum number of people is 3 (n=3).
Senior Manager
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Re: ps-leap year [#permalink]  30 May 2005, 15:46
sparky wrote:
christoph wrote:
How many randomly assembled ppl do u need to have a better than 50% prob. that at least 1 of them was born in a leap year ?

prob of being born in a leap year is 1/4 and not being born in a leap year is 3/4
(note: if considering days of birth, than probabilities will be slightly different because leap year has 366 days, so prob of being born on a leap year is 366/(3*365+366) = approx 1/4 )

prob(none out of n people is born in a leap year) is (3/4)^n

so

prob(at least one of them is born in a leap year) = 1-(3/4)^n >1/2 => (3/4)^n < 1/2

minimum number of people is 3 (n=3).

Good one sparky

I couldnt get it
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Director
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Provided I solved it right, this is a standard setup for probability-number of people problems. They all use binominal distribution. I can see this as a potential GMAT problem.
Director
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Sparky: That was a good way to solve this problem....
Manager
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heh... and now my simple way since I dont understand binomial distributions.

Leap years comes around once in every 4 years (1/4)

So some random person has a 1/4 chance of being born in a leap year.

2 people have (1/4 + 1/4) = 1/2 chance

3 peple have (1/4 + 1/4 +1/4) = 3/4 chance > 1/2

n= 3

??
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# ps-leap year

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