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# Rolling a single die

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238
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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
+26406
+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
Sort:

#1
0

You wouldn't when would you ever need to know such a thing

Guest Feb 24, 2016
#2
+5

1-(1-1/6)^11

Guest Feb 24, 2016
#4
0

How do you come to that calculation though? Thank! (So it would be ~86%?)

Guest Feb 24, 2016
#5
+26406
+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
#7
+91479
0
Melody  Mar 1, 2016

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