# A person visiting Las Vegas rolls the dice at a "craps" table and wonders what is the probability of rolling the dice 24 times without ever rolling a "7". Can the binomial distribution be applied to this situation?

Jul 14, 2016

Yes

#### Explanation:

Two dice has a probability of rolling a 7 only $\frac{2}{36}$ ways
So rolling a dice with no 7 is the same as

$\frac{34}{36}$. The probability of the 7 not landing twice in a row is $\frac{34}{36} \cdot \frac{34}{36}$ and 24 times is ${\left(\frac{34}{36}\right)}^{24}$

If we used the binomial distribution we would say

$n C k \cdot {\rho}^{k} {\left(1 - \rho\right)}^{n - k}$ thus the result would be

((24!)/((24-24)!24!)) (34/36)^24(1-34/36)^(24-24)

((24!)/(24!)) (34/36)^24(1-34/36)^(0)

you will notice that the only thing that remains is
${\left(\frac{34}{36}\right)}^{24}$

so yes you can use it.