Phil rolls 6 fair 6-sided dice. What is the probability that at least two dice show the same number?

Guest Jul 1, 2018

#1**+1 **

Are the dice all the same or all different, colours or sizes I mean?

It is complicated either way but it does make a difference.

It would be 1 - the prob of 2 not being the same.

= 1- the prob that they are all different.

If the dice are all **different** then there are 6! way that they can be all different.

If the dice are all different then there are 6^6 variations on what can be thrown.

So prob that they are all different = \(\frac{6!}{6^6}\)

and the probability that they ar not all different = \(1-\frac{6!}{6^6}\)

1-6!/(6^6) = 0.9845679012345679

so the prob that at least 2 die show the same number is about 98.5%

Melody
Jul 2, 2018