A box contains 65 balls numbered from 1 to 65. If 9 balls are drawn with replacement, what is the probability that at least two of them have the same number
This is the same mathematical problem of 2 people out of 9 sharing the same birthday! But instead of having 365 days, or 365 balls in this case, we have only 65 balls!
1 - The number of possible permutations =65 [nPr] 9 =1,160,009,419,6454,400
2 - The sample space =65^9 =2,0711,912,837,890,625
3 - P =1 - [1,160,009,419,6454,400 / 2,0711,912,837,890,625]
4 - P =43.99% - probability of 2 balls matching.
