A box contains 100 balls numbered from 1 to 100. If 13 balls are drawn with replacement, what is the probabil?

A box contains 100 balls numbered from 1 to 100. If 13 balls are drawn with replacement. What is the probability that at least two of them have the same number?A box contains 100 balls numbered from 1 to 100. If 13 balls are drawn with replacement, what is the probabil?
Instead of figuring the probability of at least two matching, let's compute the probability that *none* of them match:





P(none match):


Draw the first ball, then replace it.


The next ball has a 99/100 chance of not matching the first.


The next ball has a 98/100 chance of not matching the first two.


The next ball has a 97/100 chance of not matching the first three.


The next ball has a 96/100 chance of not matching the first four.


etc.


Repeat this for at total of 12 additional balls.





(100/100) * (99/100) * (98/100) * ... * (88/100)


鈮?0.44277496


鈮?44.3%





Remember that's the probability that none of them match. The opposite probability would be that at least two have the same number.


P(at least two match)


= 1 - P(none match)


= 1 - 0.44277496


= 0.55722504





Answer:


鈮?55.7%A box contains 100 balls numbered from 1 to 100. If 13 balls are drawn with replacement, what is the probabil?
The easiest way to calculate this is to calculate the probability of the opposite event and subtract it from 1. The probability that no balls have the same number means that for the first draw, it doesn't matter which ball is drawn, for the second draw the first ball may not be drawn again, for the third draw, the first two balls may not be drawn again etc. So the probability is





1 - (100 / 100) * (99 / 100) * (98 / 100) * ... * ((100 - 12) / 100)
1/100 or 1/9900, can't remember the math.
You need to get laid.
i don't know 13/100? haha