# Simon is rolling two fair dice. He thinks the probability of getting two sixes is 1/36. Is this correct and why or why not?

Jun 15, 2017

$\text{correct}$

#### Explanation:

$\text{the probability of obtaining a 6 is}$

$P \left(6\right) = \frac{1}{6}$

$\text{to obtain the probability of getting 2 sixes multiply the}$
$\text{probability of each outcome}$

$\text{6 AND 6 } = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$

Jun 15, 2017

$\frac{1}{36}$ is correct

#### Explanation:

There are 6 different outcomes on each die. Each outcome on one die can be combined with each outcome on the other.

This means there are $6 \times 6 = 36$ different possibilities.

However, there is only one way of getting two sixes.

So the probability of double $6$ is $\textcolor{red}{\frac{1}{36}}$

This is shown in the table below.

$\textcolor{b l u e}{\text{ "1" "2" "3" "4" "5" } 6}$

$\textcolor{b l u e}{1} : \text{ "2" "3" "4" "5" "6" } 7$

$\textcolor{b l u e}{2} : \text{ "3" "4" "5" "6" "7" } 8$

$\textcolor{b l u e}{3} : \text{ "4" "5" "6" "7" "8" } 9$

$\textcolor{b l u e}{4} : \text{ "5" "6" "7" "8" "9" } 10$

$\textcolor{b l u e}{5} : \text{ "6" "7" "8" "9" "10" } 11$

$\textcolor{b l u e}{6} : \text{ "7" "8" "9" "10" "11" } \textcolor{red}{12}$

Jun 16, 2017

He is correct.

#### Explanation:

Let's look at just one die for now. The probability for getting a $6$ on one die is $\frac{1}{6}$ since there are $6$ sides to a die, each number from $1$ to $6$ occupying a side. The other die is also the same, with numbers $1$ to $6$ occupying one side of the die. This also means that the probability of rolling a $6$ on the second die is also $\frac{1}{6}$. Combined, the probability that you roll a $6$ on both dies is

$\frac{1}{6} \cdot \frac{1}{6} = \frac{1}{36}$

This means that Simon is correct.