# 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

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

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

$\chi$ $\sigma$

MHB Math Helper