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

Guest Jul 1, 2018

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

Why would a difference in the dice (assuming it does not affect the fairness) make the probability outcomes different?  

Guest Jul 2, 2018
edited by Guest  Jul 2, 2018

17 Online Users


New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.