The probability of a die landing on some number n times in m throws

May 2010
63
0
[Solved] The probability of a die landing on some number n times in m throws

If a die is rolled 10 times, what is the probability that it lands on '6' exactly 5 times?

My approach:
There \(\displaystyle {10 \choose 5}\) ways for the number '6' to turn up 5 times in 10 throws.
The probability of a '6' appearing after each throw is 1/6.
The probability of any other number turning up after each throw is 5/6.

So I have,
\(\displaystyle P = {10 \choose 5} (1/6)^{5} (5/6)^{5}\)

Am I thinking about this the right way? Thanks.
 
Last edited:

Plato

MHF Helper
Aug 2006
22,507
8,664
Yes that is correct.
It is simple binomal probability.
 
  • Like
Reactions: director