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How many randomly assembled people do u need to have a better than 50%
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07 Nov 2022, 00:44
07 Nov 2022, 00:44
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How many randomly assembled people do you need to have a better than 50% prob. that at least 1 of them was born in a leap year?
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Re: How many randomly assembled people do u need to have a better than 50%
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02 Dec 2022, 07:56
02 Dec 2022, 07:56
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Soln: Prob. of a randomly selected person to have NOT been born in a leap yr = 3/4
Take 2 people, probability that none of them was born in a leap = 3/4*3/4 = 9/16. The probability at least one born in leap = 1- 9/16 = 7/16 < 0.5
Take 3 people, probability that none born in leap year = 3/4*3/4*3/4 = 27/64.
The probability that at least one born = 1 - 27/64 = 37/64 > 0.5
Thus min 3 people are needed.
Take 2 people, probability that none of them was born in a leap = 3/4*3/4 = 9/16. The probability at least one born in leap = 1- 9/16 = 7/16 < 0.5
Take 3 people, probability that none born in leap year = 3/4*3/4*3/4 = 27/64.
The probability that at least one born = 1 - 27/64 = 37/64 > 0.5
Thus min 3 people are needed.
Re: How many randomly assembled people do u need to have a better than 50%
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02 Dec 2022, 17:36
02 Dec 2022, 17:36
1
Carcass wrote:
Soln: Prob. of a randomly selected person to have NOT been born in a leap yr = 3/4
Take 2 people, probability that none of them was born in a leap = 3/4*3/4 = 9/16. The probability at least one born in leap = 1- 9/16 = 7/16 < 0.5
Take 3 people, probability that none born in leap year = 3/4*3/4*3/4 = 27/64.
The probability that at least one born = 1 - 27/64 = 37/64 > 0.5
Thus min 3 people are needed.
Take 2 people, probability that none of them was born in a leap = 3/4*3/4 = 9/16. The probability at least one born in leap = 1- 9/16 = 7/16 < 0.5
Take 3 people, probability that none born in leap year = 3/4*3/4*3/4 = 27/64.
The probability that at least one born = 1 - 27/64 = 37/64 > 0.5
Thus min 3 people are needed.
Thanks for posting this, would my method below work as well?
1/4 people have a chance of being born in a leap year
2 people doubles this chance (1/4 + 1/4 = 2/4 i.e. 1/2)
need at least 3 people to be LARGER than 1/2.
