The Probability Scale & Language

Grade 3

What is probability?

Probability is a way of measuring how likely something is to happen. We give every event a number between 0 and 1.

A probability of 0 means it's impossible — it will never happen. A probability of 1 means it's certain — it will definitely happen. Everything else sits somewhere in between.

You can write probability as a fraction, a decimal or a percentage — they all mean the same thing. ½ = 0.5 = 50% all say "equally likely to happen or not happen".

Words to know

Exam questions use probability language, so it pays to know these terms:

Impossible — probability 0. Unlikely — less than half. Even chance (or "evens") — exactly ½. Likely — more than half. Certain — probability 1.

If a question says "an event has an even chance", that means P = ½, not that the outcome is some particular number.

Placing events on the scale

EXAMPLE
A bag holds 3 red counters and 1 blue counter. Place these on a probability scale: (a) picking red at random, (b) picking green at random, (c) picking either red or blue.
(a) There are 3 reds out of 4 counters total: P(red) = 3/4 = 0.75. That sits between ½ and 1 — likely. (b) There are no green counters: P(green) = 0. That sits at the impossible end. (c) Every counter is either red or blue: P(red or blue) = 1 — certain.

Watch out for this

Probability can never be less than 0 or more than 1. If your answer is negative or bigger than 1, you've made an error — go back and check your fraction.
Nova
Try this one

A factory tests \( 1500 \) light bulbs. \( 36 \) of them are found to be faulty.

(a) Work out the relative frequency of a bulb being faulty. Give your answer as a decimal. [2]

(b) The factory produces \( 20\,000 \) bulbs in a week. Estimate how many will be faulty. [2]

Nova's hint:

This uses relative frequency as an estimate of probability, then applies it to a larger batch.

Ask yourself: 'what fraction of the tested bulbs were faulty, and how do I scale that up?' Once you have the relative frequency, multiply it by the larger total.

Try to Solve it with Nova?