Student resources icon

The sum of the probabilities is equal to 1

When we are about to toss a single die we know that we are certain to roll one of the numbers on the die. So the probability of rolling a 1, 2, 3, 4, 5 or 6 is certain and the total probability is 1. The probability of each outcome is \(\dfrac{1}{6}\). There are six different outcomes in this situation, so we write \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) = \(\dfrac{6}{6}\) = 1.

So the whole probability for a particular situation is 1, and we divide this whole probability into probabilities that are smaller than one and share them around over the equally likely possibilities.

Four-coloured spinner.
Detailed description

We can list the outcomes for the spinner shown:

Orange, red, green or blue.

The probability of each outcome is the same, because the area of the spinner taken up by each colour is equal.

We write the probability for each outcome as \(\dfrac{1}{4}\) because there is one way to roll each of the four colours.

The total probability for one spin of the spinner is \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) = \(\dfrac{4}{4}\) = 1.