Chance as a fraction.

Step 1 of 5

One die

A fair die has six faces, and each is as likely to come up as any other. When all the outcomes are equally likely, the probability of an event is a fraction: the number of outcomes that fit the event on top, and the number of all the outcomes underneath. If $k$⁠ out of $n$⁠ outcomes fit,

$P = \frac{k}{n}$⁠

The board shows the six faces. The event is “a $5$⁠ or more”. Predict its probability, then watch which faces light up.

Step 2 of 5

A total of $2$⁠ or of $7$⁠?

Now roll two dice and add them. Each square of the table carries its total, and the $36$⁠ squares are the equally likely outcomes.

The totals themselves, $2$⁠ to $12$⁠, are not equally likely: each total has a different number of squares. The board lights the only square with a total of $2$⁠. Which total is more likely, $2$⁠ or $7$⁠?

Step 3 of 5

The chance of a total of $8$⁠

Count the squares in the table whose total is $8$⁠. The probability is that number out of $36$⁠, and as in the Lesson on percentages, you can write it as a fraction, a decimal or a percentage.

Step 4 of 5

A chance of one in twelve

Now the other way round: the chance is given, and you look for an event. Change Total and find a total whose chance is exactly $\frac{1}{12}$⁠.

Step 5 of 5

The complement

The chance that something does not happen is everything that is left: the squares that are not lit. Since all the squares together make $\frac{36}{36} = 1$⁠, the chance that an event $A$⁠ does not happen is

$1 - P(A)$⁠

The event “$A$⁠ does not happen” is called the complement of $A$⁠. Sometimes it is easier to count the complement and take it away from $1$⁠.