dice question

[chappo11]

if rolling a single die - the odds of rolling a one one time is 1/6 or 16.6%. if you were to roll a die six times, what are the odds you would roll a one twice? what are the odds you would roll a one three times, and get the three rolls that were any number but one? what are odds of four ones, and two non ones during the six rolls?

 

[tkhunny]

It is Binomial

\(\displaystyle p(0) = {{6}\choose{0}}\left(\frac{1}{6}\right)^{0}\left(\frac{5}{6}\right)^{6}
\)
\(\displaystyle p(1) = {{6}\choose{1}}\left(\frac{1}{6}\right)^{1}\left(\frac{5}{6}\right)^{5}\)

etc.

 

[pka]

if rolling a single die - the odds of rolling a one one time is 1/6 or 16.6%. if you were to roll a die six times, what are the odds you would roll a one twice? what are the odds you would roll a one three times, and get the three rolls that were any number but one? what are odds of four ones, and two non ones during the six rolls?

If we roll a die N times and \(\displaystyle 0\le k\le N\) then the probability of exactly k ones is \(\displaystyle \displaystyle\binom{N}{k}\left(\frac{5^{N-k}}{6^N}\right)\)

 

[soroban]

Hello, chappo11!

If rolling a single die, the probabiity of rolling a one one time is 1/6.

if you were to roll a die six times, what is the probability you would roll a one twice?

\(\displaystyle \displaystyle P(\text{two 1's, four Others}) \:=\:{6\choose2}\!\left(\frac{1}{6}\right)^2\!\left(\frac{5}{6}\right)^4\)

What is the probability you would roll a one three times,
and get the three rolls that were any number but one?

\(\displaystyle \displaystyle P(\text{three 1's, three Others}) \:=\:{6\choose3}\!\left(\frac{1}{6}\right)^3\!\left(\frac{5}{6}\right)^3\)

What is the probablity of four ones, and two non-ones during the six rolls?

\(\displaystyle \displaystyle P(\text{four 1's, two Others}) \:=\:{6\choose4}\!\left(\frac{1}{6}\right)^4\!\left(\frac{5}{6}\right)^2\)