Balls Boxed
Balls Boxed
One box contains 100 balls numbered from 1 to 100. If 13 balls are drawn with replacement, what is the probability?
One box contains 100 balls numbered 1 to 100. If 13 balls are drawn with replacement. What is the probability that at least two of them have the same number?
Instead of calculating the probability at least two overlapping Let us calculate the probability that * are * no match: P (none match): Draw the first ball, then replace it. The next ball has a 99/100 chance that do not match the first. the next ball has a 98/100 chance that do not coincide with the first two. The next ball is 97/100 possibility that one may not match the first three. the next ball has a 96/100 chance of not matching the top four. etc. Repeat this step for the total of 12 balls additional. (100/100) * (99/100) * (98/100) * ... ≈ * (88/100) ≈ 0.44277496 Remember that 44.3% of the probability that none of them match. Otherwise the probability would be at least two have the same number. P (at least two match) = 1 - P (no match) = 1 - 0.44277496 = 0.55722504 Answer: ≈ 55.7%
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