Probability scale and basics

Measure chance from 0 to 1, calculate probabilities of equally likely outcomes and use the fact that all probabilities add to 1.

About 3 min read
  • Place events on the probability scale
  • Calculate the probability of an event
  • Find the probability that an event does not happen
  • Use relative frequency to estimate probability
Before you start

You can simplify fractions and convert between fractions, decimals and percentages. Probabilities are written in all three forms.

The probability scale

Probability measures how likely something is. It always lies between 0 and 1. A probability of 0 means the event is impossible, and 1 means it is certain. An event with probability 0.5 is as likely to happen as not to happen.

Definition: outcome

One possible result of an experiment, such as rolling a 4 on a dice.

Definition: event

One or more outcomes that you are interested in, such as rolling an even number.

Calculating probability

When all outcomes are equally likely, use this formula:

Probability of an event

P(event) = number of favourable outcomes ÷ total number of outcomes

An event either happens or does not happen, so P(not A) = 1 − P(A).

Relative frequency

Some probabilities cannot be calculated from equally likely outcomes. A drawing pin may land point up or point down, but those outcomes are not equally likely. We can estimate the probability from an experiment: relative frequency equals the number of successes divided by the number of trials. More trials usually give a better estimate.

Coloured counters

A bag has 3 red, 5 blue and 2 green counters. One is taken at random. Find P(blue) and P(not green).

Maths
total counters = 3 + 5 + 2 = 10
P(blue) = 5/10 = 1/2
P(green) = 2/10 = 1/5
P(not green) = 1 − 1/5 = 4/5

Answer: P(blue) = 1/2 and P(not green) = 4/5.

Check your answer

A probability can never be negative or greater than 1. If yours is, there is a mistake in the working.

Exam focus
Say it like this“P(red) = 3/10”
Not like this“P(red) = 3 out of 10” — Write probabilities as a fraction, decimal or percentage, not in words.
Common mistakeUsing the number of other outcomes as the denominator instead of the total number of outcomes.

Practice

A fair dice is rolled. Find P(a number greater than 4).
5 and 6 are favourable, so P = 2/6 = 1/3.
The probability of rain is 0.35. Find the probability of no rain.
1 − 0.35 = 0.65.
A pin lands point up 36 times in 120 throws. Find the relative frequency.
36/120 = 0.3.
Going further
A spinner has P(red) = 2x, P(blue) = 3x and P(green) = 0.5. Find x.
2x + 3x + 0.5 = 1, so 5x = 0.5 and x = 0.1.

Quick check

Probability quick check

What is the probability of a certain event?

The scale ends at this value, which means the event always happens.

A letter is chosen from the word MATHS. What is P(a vowel)?

Only A is a vowel, and there are five letters to choose from.

P(win) = 0.2. What is P(do not win)?

Winning and not winning cover everything, so subtract 0.2 from 1.
Key takeaways
  • Probability runs from 0 to 1.
  • For equally likely outcomes, divide favourable outcomes by total outcomes.
  • P(not A) = 1 − P(A).
  • Relative frequency estimates probability from experiments.
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