If each person randomly gets a number between 1 and 10
then how many many people do you need together for there to be more than a 50 percent chance for two of them to have the same number.
Show how you did it please!
then how many many people do you need together for there to be more than a 50 percent chance for two of them to have the same number.
Show how you did it please!
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Consider the probability that no two have the same number.
If there is one person, the probability is 10/10 = 1.
If there are two people, the probability is 10/10 * 9/10.
... three people, the probability is 10/10 * 9/10 * 8/10
and so on.
So the question becomes this: what is the smallest number k such that
(10 * 9 * ... * (10-k+1)) / 10^k < 1/2.
I don't know of a good way to do this, but if you start testing them, you'll find that
(10 * 9 * 8 * 7) / 10^4 = 0.504
(10 * 9 * 8 * 7 * 6) / 10^5 = 0.3024
Therefore the answer is 5 people. Note, though, that with 5 people the probability that some two have the same number is given by
1 - 0.3024 = 0.6976
If there is one person, the probability is 10/10 = 1.
If there are two people, the probability is 10/10 * 9/10.
... three people, the probability is 10/10 * 9/10 * 8/10
and so on.
So the question becomes this: what is the smallest number k such that
(10 * 9 * ... * (10-k+1)) / 10^k < 1/2.
I don't know of a good way to do this, but if you start testing them, you'll find that
(10 * 9 * 8 * 7) / 10^4 = 0.504
(10 * 9 * 8 * 7 * 6) / 10^5 = 0.3024
Therefore the answer is 5 people. Note, though, that with 5 people the probability that some two have the same number is given by
1 - 0.3024 = 0.6976
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Well if its random then every 10 people should statistically have a number between 1 and 10....
So you'll never have a 50 percent chance if the numbers are truly random.
So you'll never have a 50 percent chance if the numbers are truly random.
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Ask you parents or something