With the goal of using an Excel formula for dice probability, how do I calculate the probability of rolling a 7 or greater at least 3 times out of 10 using a D10 dice?

Answer 1

The probability of a 7, 8, 9 or 10 is 0.4 (let’s call this event a “success” and so the probability of a 1 to 6 is 0.6.

Therefore the probability of n “successes” out of ten rolls of the D10 die, from the general binomial formula is:

0.4^n * 0.6^(10-n) * 10Cn

Where 10Cn=10!/(n!*(10-n)!)

To get the probability that there are at least three “successes” out of 10, you will need to sum the above over values of n from 3 to 10.

(Alternatively take 1 minus the probability of 0, 1 or 2 “successes”).