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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

 Aug 14, 2020
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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.

 Aug 14, 2020

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