# What is the probability of rolling a sum of 10 with two dice?

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39
Jul 9, 2017

$P \left(10\right) = \frac{1}{12}$

#### Explanation:

If you roll two dice, there are $6 \times 6 = 36$ possible outcomes.

There are only three different ways of getting a total of $10$

$4 + 6 = 10$
$5 + 5 = 10$
$6 + 4 = 10$

"Probability of an event" = ("number of desirable outcomes")/("total number of possible outcomes")

$P \left(10\right) = \frac{3}{36} = \frac{1}{12}$

Then teach the underlying concepts
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#### Explanation

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6
Jul 9, 2017

$\frac{1}{12}$

#### Explanation:

6 & 4, 5 & 5, 4 & 6.

Each has probability $\frac{1}{36}$ so aggregate is $\frac{3}{36} = \frac{1}{12}$

The following chart shows the probability of throwing $n$ with two dice.

The more dice you throw, the more this distribution tends towards a normal distribution.

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