The Language of Chance

14 min

Let's begin

Every evening the radio reads the weather forecast: "Heavy rain is likely in the Northern Province tomorrow." Not "certain", only "likely".

Many things in life may or may not happen: rain on umuganda day, your team scoring at break, a seed growing into a tree. In this lesson you will learn the words we use to say how likely something is, and a line to put them on.

Chance experiments, outcomes and events

A chance experiment is anything whose result you cannot know in advance: tossing a coin, rolling a die, or picking a bean from a bag without looking.

Each possible result is an outcome. Rolling a die has six outcomes: 1, 2, 3, 4, 5 and 6.
An event is one or more outcomes that we are interested in. "Rolling an even number" is the event made of the outcomes 2, 4 and 6.

Words for chance

Word	Meaning	Example
Impossible	cannot happen at all	a cow laying an egg; rolling a 7 on a normal die
Unlikely	could happen, but probably will not	picking the one red bean from a bag of 1 red and 9 white beans
Even chance (equally likely)	just as likely to happen as not to happen	a tossed coin landing on heads
Likely	will probably happen, but might not	picking a white bean from that same bag
Certain	must happen	the sun setting this evening; rolling a number less than 7 on a die

Rwanda's seasons give good examples too. On a day in April, in the long rainy season, rain in Kigali is likely. On a day in July, in the long dry season, rain is unlikely, but not impossible.

Two outcomes are equally likely when they have the same chance, like heads and tails. We also compare events by saying one is more likely or less likely than another.

The likelihood line

We can put events on a line that runs from impossible at one end to certain at the other, with even chance exactly in the middle. Later you will see that the ends are the numbers 0 and 1, and the middle is ½.

Worked example

three bags of beads.

Bag 1 has 3 red and 3 blue beads. Red and blue are equally likely, so picking red is an even chance.
Bag 2 has 5 red beads and 1 blue bead. Picking red is likely; picking blue is unlikely.
Bag 3 has 6 blue beads. Picking blue is certain; picking red is impossible.

Tip

Ask three questions in order:

Can it happen at all? If not, it is impossible.
Must it happen? If yes, it is certain.
Otherwise: does it happen more than half the time (likely), less than half (unlikely), or exactly half (even chance)?

✦

Try it yourself

Choose impossible, unlikely, even chance, likely or certain.

Tomorrow will come after today.
You roll a 3 on a fair die.
A fair coin lands on tails.
You pick a green sweet from a bag of 8 green sweets and 2 red sweets.
You roll a 0 on a normal die.

Answers

Certain.
Unlikely: only 1 of the 6 faces is a 3.
Even chance.
Likely: 8 of the 10 sweets are green.
Impossible: a normal die has no 0.

Quick check

A bag has 9 blue beads and 1 yellow bead. You pick one without looking. How likely is it to be yellow?

What you learned today

A chance experiment has outcomes; an event is one or more of those outcomes.
The words of chance, in order: impossible, unlikely, even chance, likely, certain.
Events can be placed on a likelihood line from impossible to certain, with even chance in the middle.

Sources and credits

IM 6–8 Math, Grade 7, Unit 8, Lesson 2: Chance Experiments by Illustrative Mathematics (originally developed by Open Up Resources), licensed under CC BY 4.0. Adapted by Ganzaa.

Written by Ganzaa: the likelihood-line drawing, the table of Rwandan examples and the bead-bag worked example. No openly licensed P6 reading on the likelihood scale was found, so these parts are Ganzaa's own; the words for chance and the idea of outcomes and events are adapted from Illustrative Mathematics.

1Chance experiments, outcomes and events

2Words for chance

3The likelihood line

Try it yourself

Chance experiments, outcomes and events

Words for chance

The likelihood line