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If you roll a 10 sided die 3 times how to calculate the odds of it landing on 10 exactly twice?
0 times: 90% chance to not land -> .9^3
1 times: 1-.9^3 - (odds of it landing 2 or 3 times)
2 times: This is what I want to know how to calculate
3 times: .1^3
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>>1556173
the chance of 10 multiplied by the chance of 10 multiplied by the chance of not-10 gives you the chance of each individual arrangement of 2 successes and 1 failure, in this case, SSF
you then need to multiply this by the number of possible arrangements of 2 successes and 1 failure, which is three
SSF
SFS
FSS
thus 3 x 0.1 x 0.1 x 0.9 = 0.027
also, you're wrong about the chance of 1 ten. your formula gives 0.271, but the correct formula (same as above) gives 0.243. yours is the chance of AT LEAST ONE 10.
the full formula is here
https://en.wikipedia.org/wiki/Negative_binomial_distribution#Probabili ty_mass_function