### Edexcel GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Introduction to Probability

The probability of an event is a measure of how likely that event will happen. It is normally measured in either fractions, percentages, or decimals.

For example, if a coin is flipped, it’s equally likely to land on heads or tails. As there are only two outcomes, the chance of the coin landing on either heads or tails is 50%.

## Calculating Probability

When calculating the probability of an event occurring, you need to know two things:

• The number of times or ways the event could occur
• The total number of possible events

For example, if I roll a standard 6-sided dice, what is the probability that it lands on a 2?

1. How many ways could this event occur? Only one way, as there is only one 2 on the dice.

2. How many events (or possibilities) is this out of? On the dice, there are 6 different numbers that it could have landed on. Therefore, this is out of 6 possibilities. Now write the probability as a fraction, with the first number on top, and the total number of possibilities on the bottom:

## Probability Scales

Probability can also be displayed on a probability scale from 0 to 1. The closer the probability is to 0, the less likely it will be, and the closer it is to 1, the more likely it will be. For example, in a standard deck of cards, there are 4 different suits.

The probability of randomly selecting a card that is a heart out of the deck is , or 0.25. This can be shown on the scale with an arrow:

If we wanted to find the probability of selecting just a red card, there would be two options (hearts or diamonds) out of the 4 suits. Therefore, this probability would be \frac{2}{4}, which simplifies to \frac{1}{2}, or 0.5.

When we add this to the scale, it becomes clear that the probability of selecting a red card is more likely than the probability of selecting a heart.