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Jack rolls 5 fair six-sided dice. What is the probability that at least two dice show the same number?

please help quickly

 Aug 26, 2018
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First die: any number

2nd die : 5/6 probability that it is different from the first

3rd die  : 4/6 probability that it is different from the first two

4th die  : 3/6 probability that it is different from the first three

5th die  : 2/6 probability that it is different from the first four

So, the probability that they are all different from each other is:

6/6 x 5/6 x 4/6 x 3/6 x 2/6 =720 / 6^5. Therefore:

The probability that at least two of them show the same face is:

1 - 720/ 7,776 =7,056 / 7,776 =49 / 54 =90.74%

 Aug 26, 2018

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