Question

A die is rolled 12 times. Find the chance that the face with six spots appears once among the first 6 rolls, and once among the next 6 rolls.

Answer 1

i think it is a binomil probability
what do u think?

Answer 2

..yes it is

Answer 3

i tried FFFFFS ie (5/6)^5*(1/6)^1
and FFFFFFFFFFFS ie (5/6)^11*(1/6)^1
then the product of the two but its not quite correct

Answer 4

so the probability of sucess is
1/6 right?

Answer 5

The results of first six rolls and second six rolls are totally independent. The probability of getting one specific face is 1/6. To get only this face in six rolls can be calculated with Binomial Distribution:\[P(k)=\left(\begin{matrix}n \\ k\end{matrix}\right)p^k(1-p)^{n-k}=\left(\begin{matrix}6 \\ 1\end{matrix}\right)\left( \frac{ 1 }{ 6}\right)^1\left( \frac{ 5 }{ 6} \right)^5=\left( \frac{ 5 }{ 6 } \right)^5\] As it has to happen in first and second rounds, then the probability is:\[\left( \frac{ 5 }{6 } \right)^5\left( \frac{ 5 }{6 } \right)^5=\left( \frac{ 5 }{6 } \right)^{10}=0.1615\]

Answer 6

this is correct,thanks