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