# Die Rolling Probability

#### Essential06

##### New member
Can anyone help me with this one please...

If i roll a dice 100 times and number 6 comes out on 14 occassions (14%) what would have been the probability of number 6 being rolled 4 times in a row? (as a percentage?)

If someone would be so kind to tell me how to calculate this in simple terms i'd be really grateful. Thanks

#### Sudharaka

##### Well-known member
MHB Math Helper
Re: Probability Help Please

Can anyone help me with this one please...

If i roll a dice 100 times and number 6 comes out on 14 occasions (14%) what would have been the probability of number 6 being rolled 4 times in a row? (as a percentage?)

If someone would be so kind to tell me how to calculate this in simple terms i'd be really grateful. Thanks
Hi Essential06,

Let me summarize the method that I will use to solve this problem.

Find the number of arrangements with 6 rolling out on 14 occasions(we shall take this as $$x$$). Then among those outcomes with 14 sixes find the number of arrangements where 6 is rolled 4 times in a row(we shall take this as $$y$$). Supposing that each outcome with 6 being rolled 4 times in a row is equally likely to happen,

The probability of getting 6 rolled 4 times in a row is, $$\dfrac{y}{x}$$.

Hope you can continue.

Kind Regards,
Sudharaka.

#### chisigma

##### Well-known member
Re: Probability Help Please

Can anyone help me with this one please...

If i roll a dice 100 times and number 6 comes out on 14 occassions (14%) what would have been the probability of number 6 being rolled 4 times in a row? (as a percentage?)

If someone would be so kind to tell me how to calculate this in simple terms i'd be really grateful. Thanks
If p is the probability of the number six in each roll, then the probability to have 4 six in 10 rolls is,,,

$\displaystyle P= \binom {10}{4} p^{4}\ (1-p)^{6}$ (1)

If the dice is 'non loaded' then is $\displaystyle p=\frac{1}{6} = .16666666666...$ and that is compatible with 14 six in 100 rolls. If $\displaystyle p=\frac{1}{6}$ then the (1) gives $\displaystyle P= .05426587585...$...

Kind regards

$\chi$ $\sigma$

#### Plato

##### Well-known member
MHB Math Helper
Re: Probability Help Please

If i roll a dice 100 times and number 6 comes out on 14 occassions (14%) what would have been the probability of number 6 being rolled 4 times in a row? (as a percentage?)
I for one would like you to explain exactly what this question means.
Are you asking about exactly one run of four 6's?
Or could there be three runs of four 6's.? If so do they have to be separated?
If not how do you count a run of six 6's?
This question is so ill-defined as to be unanswerable.