How would you calculate the probability of rolling a single die 11 times and getting all of the numbers at least once.

Guest Feb 24, 2016

#5**+5 **

I've done a Monte-Carlo simulation on this which suggests the probability of getting all the numbers at least once is about 0.356.

I selected 11 numbers uniformly and randomly from the digits 1 to 6. I then looked to see if all the digits from 1 to 6 were present. If they were all present I increased a running total (that started at zero) by 1; if they weren't all present I didn't increase the running total. I repeated this two million times and calculated the probability as running total/two million.

.

Alan
Feb 26, 2016

#5**+5 **

Best Answer

I've done a Monte-Carlo simulation on this which suggests the probability of getting all the numbers at least once is about 0.356.

I selected 11 numbers uniformly and randomly from the digits 1 to 6. I then looked to see if all the digits from 1 to 6 were present. If they were all present I increased a running total (that started at zero) by 1; if they weren't all present I didn't increase the running total. I repeated this two million times and calculated the probability as running total/two million.

.

Alan
Feb 26, 2016