# Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 6

GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 6

02:20

### Video Transcript

Ryan rolls a fair six-sided die numbered from one to six. Part a) Using a cross, mark on the probability scale the probability of rolling an even number.

A probability scale is used to show the chance or likelihood of an event occurring. Events that are impossible have a probability of zero and events that are certain to happen have a probability of one. Other events are placed on the scale according to the probability of them occurring.

In part a of this question, we were asked about the probability of rolling an even number on a fair six-sided die, which has faces numbered from one to six. The keyword in this question is “fair,” which means that the die has an equal probability or chance of landing on each face. And therefore, the outcomes of one, two, three, four, five, and six are all equally likely to occur.

There are three even numbers: two, four, and six. And as each of these numbers are equally likely, this means that the probability of scoring a two, a four, or a six is three out of six or three-sixths. This fraction can be cancelled down by dividing both the numerator and denominator by three to give one over two or one-half.

We can, therefore, put this cross in the very center of our probability scale, at a probability of one-half.

Now, let’s look at the second part of this question.

Part b) says, “Using a cross, mark on the probability scale the probability of rolling a number less than four.” So we have the same setup as before, which means the possible outcomes are the numbers one, two, three, four, five, and six all with an equal chance of occurring. The numbers which are less than four so that strictly less than four, not including four itself are one, two, and three.

So again, we have three out of six possible outcomes, which gives a fraction of three over six, which can be simplified to one-half. The cross for part b also goes in the very center of the probability scale.