AC9M4P01 · YEAR 4 · PROBABILITY

Likelihood and Independent Events

ACARA v9 CONTENT DESCRIPTION describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events
Builds on: Repeated Chance Experiments (AC9M4P02). This unit describes everyday events and the outcomes of chance experiments, orders them by likelihood, and introduces independent and dependent events.

The chance scale

Every event can be placed on a scale of chance, from impossible at one end, through an even chance in the middle, to certain at the other. The sun rising tomorrow is certain; a dog flying is impossible; a coin landing heads is an even chance. Describing events with this language — impossible, unlikely, even chance, likely, certain — is where probability begins. Year 4 places everyday events and the outcomes of experiments on this scale, building the vocabulary needed to compare and order how likely different things are.

The chance scale
Every event sits somewhere from impossible, through even chance, to certain.
Where on the scale does "the sun will rise tomorrow" belong?

Ordering by likelihood

Once events can be placed on the chance scale, they can be ordered: least likely first, most likely last. Rolling a 6 on a die is less likely than rolling an even number, which is less likely than rolling a number under 7 (which is certain). Putting events in order of likelihood sharpens the comparison, turning rough words into a definite sequence. This ordering is exactly what the curriculum asks — arranging outcomes and events by their chance of occurring — and it builds the judgement needed to reason about probability sensibly.

Ordering by likelihood
Events can be put in order from least likely to most likely.
These three events have different chances. Order them from least to most likely.

Possible outcomes

Describing a chance experiment means listing all the things that could happen: its possible outcomes. Flipping two coins gives four outcomes — HH, HT, TH, TT. Rolling a die gives six. Knowing every possible outcome is the basis for judging how likely each is, because chance compares what could happen against what we are interested in. Setting out the outcomes of an experiment clearly, before reasoning about likelihood, is a habit this unit builds, and it connects everyday chance language to the more careful listing that probability needs.

Possible outcomes
Describing a chance experiment means listing all its possible outcomes.
Flip two coins. What are all the possible outcomes?

Independent events

Some events do not affect one another: these are independent. Each flip of a coin is independent, because the coin has no memory — after three heads, the next flip is still an even chance. The same is true of rolling a die again, or spinning a spinner: the previous result changes nothing. Recognising independence corrects a common mistake, the feeling that a run of heads makes tails "due". Year 4 begins to identify independent events, an idea that matters whenever the same experiment is repeated and each try stands on its own.

Independent events
In independent events, one result does not change the chance of the next.
However many heads or tails have come up, the next flip is still an even chance. A coin has no memory: each flip is independent, unaffected by the results before it.

Dependent events

Other events do affect one another: these are dependent. Draw a marble from a bag and keep it, and the next draw faces a changed bag — fewer marbles, different chances. Dealing cards works the same way: each card dealt changes what is left. Here the first result does change the second, the opposite of the coin. Telling dependent from independent events — asking whether the first outcome alters the chances of the next — is the key new idea of this unit, and it is the question to ask of any two events in sequence.

Dependent events
In dependent events, one result changes the chance of the next.
A bag of 5 marbles. Draw one out and keep it. What happens to the next draw?

Independent or dependent?

Pulling the unit together, events can be described and ordered by likelihood, their outcomes listed, and pairs of events sorted into independent or dependent. Flipping or rolling again is independent; drawing or dealing without replacing is dependent. A table makes the sorting plain, and the single question behind it — does the first result change the chances of the next? — settles every case. With chance language, ordering by likelihood, listing outcomes, and the independent-or-dependent distinction, a child has the core ideas of Year 4 probability, ready to study how repeated experiments behave.

Independent or dependent?
Events are independent if the first does not change the next, dependent if it does.
Is each event independent or dependent? Reveal each.
Quick self-check
1. On a scale from impossible to certain, "the sun will rise tomorrow" is...
2. Flipping a coin twice: the second flip is...
3. You draw a marble from a bag and keep it, then draw again. The two draws are...
4. Ordering events from least to most likely means putting first the event that is...
5. The difference between independent and dependent events is whether...
Teaching pack: free to printReady-to-teach plans, student sheets, cut-outs and answers for this unit. Print or save as PDF.