Dice Probabilties

Quote: Swlong1981

First time posting, I have 2 questions.

In 15 rolls of a a 6 sided die, what is the probability that any 1 number does not appear?

What I am more interested in is if you didn't have to choose which number will not appear, what is the overall chance of any specific number not showing up.

Thanks in advanced for your answers.

p = 1/6
n = 15
stat: number of different values

      group        middle      freq  freq/100
---------------------------------------------
1.50 <= x < 2.50     2.00        11     0.00%
2.50 <= x < 3.50     3.00      6146     0.06%
3.50 <= x < 4.50     4.00    324968     3.25%
4.50 <= x < 5.50     5.00   3227537    32.28%
5.50 <= x < 6.50     6.00   6441338    64.41%

---------------------------------------------
                     2.00        11
                     3.00      6146
                     4.00    324968
                     5.00   3227537
                     6.00   6441338
---------------------------------------------
                 cumulative
---------------------------------------------
1.50 <= x < 2.50     2.00        11     0.00%
2.50 <= x < 3.50     3.00      6157     0.06%
3.50 <= x < 4.50     4.00    331125     3.31%
4.50 <= x < 5.50     5.00   3558662    35.59%
5.50 <= x < 6.50     6.00  10000000   100.00%

---------------------------------------------
                     2.00        11
                     3.00      6157
                     4.00    331125
                     5.00   3558662
                     6.00  10000000

Quote: Ayecarumba

Homework?

The probability any one number not appearing in a single roll of a six sided die is 5/6. The odds of it not appearing in 15 rolls is (5/6)^15. This is the same whether a single die is rolled 15 times in sucession, or five dice are thrown three times, as each roll is independent.

If it doesn't matter which number, I think you multiply the above by 6 to get the probability of any of the six numbers not appearing in 15 rolls. But that is just a guess on my part.

Quote: Swlong1981

Thanks for the quick response.

I assure you it's not homework, just a question that came up around the office. We have been playing shake a day in the office, which no one has one yet, and have been trying to come up with other "games" with the 5 dice.

So my understanding is that ~35% of the time at least one number will not show up when you roll 5 dice 3 times?