Likelihood of Events

Lessons

Primary 6 · Mathematics

Likelihood of Events

3 lessons

Lesson 2 of 3

Chance as a Number: Probability

18 min

Let's begin

At the school fundraiser, Uwase closes her eyes and reaches into a basket. Inside are 4 avocados and 6 mangoes. Is she more likely to pull out a mango? Yes. But how much more likely?

Words like "likely" cannot answer that. In this lesson you will learn to give chance a number, called its probability.

List all the outcomes

First, list everything that could happen:

tossing a coin: heads, tails (2 outcomes);
rolling a die: 1, 2, 3, 4, 5, 6 (6 outcomes);
Uwase's basket: 10 fruits, so 10 outcomes.

Picking at random (without looking or choosing) means every outcome is equally likely.

Probability as a fraction

When all the outcomes are equally likely:

probability of an event = number of outcomes that give the event ÷ total number of outcomes

We write it P(event).

Worked example 1

Uwase's basket.

Total outcomes: 4 + 6 = 10 fruits.
P(avocado) = 410 = 25. As a decimal that is 0.4, and as a percentage 40%.
P(mango) = 610 = 35, which is 0.6 or 60%. So a mango is more likely, by 0.6 to 0.4.

Worked example 2

a fair die.

P(4) = 16, because one face out of six shows 4.
P(even number) = 36 = 12, because 2, 4 and 6 are even.
P(number greater than 4) = 26 = 13, because only 5 and 6 are greater than 4.

Worked example 3

a spinner has 8 equal parts, and 3 are blue. P(blue) = 38.

From 0 to 1

An impossible event has probability 0: rolling a 7 on a die is 06 = 0.
A certain event has probability 1: rolling a number from 1 to 6 is 66 = 1.
An even chance is 12.

A probability can never be less than 0 or more than 1. As a percentage, it is always from 0% to 100%.

The chance that something does NOT happen

An event either happens or it does not, so the two probabilities add up to 1:

P(not A) = 1 − P(A)

Worked example 4

a bag holds 3 red, 2 blue and 5 green beads. P(green) = 510 = 12, so P(not green) = 1 − 12 = 12. Check by counting: 3 red + 2 blue = 5 beads that are not green, and 510 = 12. ✔

A pack of playing cards

Some questions use a pack of 52 playing cards. It has 4 suits (hearts, diamonds, clubs and spades) of 13 cards each: ace, 2 to 10, jack, queen and king. So P(heart) = 1352 = 14, and P(king) = 452 = 113.

Tip

Probability = what you want ÷ everything that could happen. Simplify the fraction, and check that your answer is between 0 and 1.

✦

Try it yourself

What is the probability of getting tails when you toss a fair coin?
A fair die is rolled. What is the probability of a number less than 3?
A bag has 2 red, 3 yellow and 5 green sweets. What is P(yellow)?
Using the same bag, what is P(not yellow)?
What is the probability of rolling an 8 on a normal die?

Answers

12
1 and 2 are less than 3: 26 = 13.
3 of the 10 sweets: 310.
1 − 310 = 710.
0: it is impossible.

Quick check

A bag holds 3 red, 5 blue and 2 green beads. You pick one at random. What is P(blue)?

What you learned today

When outcomes are equally likely, probability = favourable outcomes ÷ total outcomes.
Probabilities go from 0 (impossible) to 1 (certain); an even chance is 12.
P(not A) = 1 − P(A).

Sources and credits

IM 6–8 Math, Grade 7, Unit 8, Lesson 3: What Are Probabilities? by Illustrative Mathematics (originally developed by Open Up Resources), licensed under CC BY 4.0. Adapted by Ganzaa.
Prealgebra 2e, 5.6 Averages and Probability by OpenStax, via LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Three six-sided dice.jpg by PierreSelim, via Wikimedia Commons, CC BY 3.0. Used unchanged.

The fruit-basket, spinner and bead examples and the note on playing cards were written by Ganzaa.

1List all the outcomes

2Probability as a fraction

3From 0 to 1

4The chance that something does NOT happen

5A pack of playing cards