Question 237881: A box contains 65 balls numbered from 1 to 65. If 10 balls are drawn with replacement, what is the probability that at least two of them have the same number?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A box contains 65 balls numbered from 1 to 65. If 10 balls are drawn with replacement, what is the probability that at least two of them have the same number?
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# of ways to pick a number: 65
probability of picking any particular number: (1/65)
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With replacement means the draw results are independent.
This is a binomial problem with n=10, p=1/65, 2<= x <= 65
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Ans P(2 <= x <= 65) = 1-[P(x=0)+P(x=1)]
= 1 - 10C0(1/65)^0(64/65)^65 + 10C1(1/65)^1*(64/65)^64]
= 1 - 0.99019 = 0.0.00981
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Cheers,
Stan H.
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