SOLUTION: 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?

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?
-----------
# of ways to pick a number: 65
probability of picking any particular number: (1/65)
------------
With replacement means the draw results are independent.
This is a binomial problem with n=10, p=1/65, 2<= x <= 65
----
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
================================
Cheers,
Stan H.
RELATED QUESTIONS
A box contains 50 balls numbered from 1 to 50. If 10 balls are drawn with replacement,... (answered by stanbon,Alyrian)

A box contains 14 balls, numbered 1 through 14. Suppose 5 balls are selected without... (answered by Edwin McCravy)

A box contains ten balls numbered from 1 to 10. If you pick two balls at random, what is... (answered by galactus,Alan3354)

a box contains 12 balls of which 4 are green and 8 are red. if 7 balls are drawn from the (answered by Edwin McCravy)

A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random without... (answered by ikleyn,greenestamps)

A box contains eleven balls, numbered 1,2,3�.10,11,11. if 6 balls are drawn... (answered by robertb)

A box contains three blue balls and three white balls. if two balls are drawn one at a... (answered by stanbon)

A box contains 2 black balls and 3 gold balls. 2 balls are randomly drawn in succession... (answered by rfer)

A box contains two black balls and three gold balls. Two balls are randomly drawn in... (answered by jim_thompson5910)