# Algebra/Probability

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Probability is the chance that something will occur. For example, what are the chances that two dice rolled will equal 7? To solve this, a chart can be made of all the pairs of the integers {1, 2, 3, 4, 5, 6} that add up to 7.

- 1 + 6
- 2 + 5
- 3 + 4
- 4 + 3
- 5 + 2
- 6 + 1

note that the first three seem to be the same as the second three. This is because there are two dice, so when the first die gets number X and the second gets Y, it's a different outcome than the first being Y and the second X.

Next, we find out how many possibilities there are in total.

6 possibilities for the first die * 6 possibilities for the second = 36 combinations.

Since 6 out of the 36 combinations add up to 7, the answer is 1/6 or 16.6666666...% or 0.166666666... Usually, probabilities are measured in the first or second way.

### Ratios[edit]

Quite often, ratios are used to show the probability of an event occurring compared to another event. Be careful! The ratio of heads to tails is 1:1 or 1/1, but the probability of heads is 1:2 or 1/2. Don't confuse these two ways of writing the same thing.