ACARA v9 CONTENT DESCRIPTION “identify possible outcomes of chance experiments involving two steps, and distinguish events whose chances are unaffected by previous results from those that are affected”
Chance gets richer when two things happen, like tossing a coin twice or drawing two marbles. The first job is to list every possible outcome of the pair. Two coins can land HH, HT, TH or TT — four outcomes in all. Listing them carefully, missing none, is the foundation for thinking about two-step chance, because you cannot judge how likely something is until you know everything that could happen. Year 4 learns to map out the outcomes of two events, and then to ask a new and important question about how the two events relate.
Two coins, all outcomes
Listing every possible result is how a chance situation is mapped out.
Toss two coins. List every result that could happen. Reveal them one at a time.
When the first does not matter
Some pairs of events do not affect each other at all. Toss a coin, then toss it again: the coin has no memory, so the second toss is still fifty-fifty no matter how the first landed. Events like this are called independent — the result of one does not change the chances of the other. Rolling a die and then spinning a spinner is the same: two separate actions that have nothing to do with each other. Recognising independence matters because it tells you the second chance is exactly what it always was, unchanged by what came before.
Independent: coins
Two events are independent when one result does not affect the other.
Toss a coin twice. Does the first result change the chance of the second?
When the first changes the second
Other pairs of events are linked. Take a marble from a bag of three red and two blue and keep it, and the bag is different for the next draw: fewer marbles, and maybe fewer red. Events like this are called dependent — the first outcome changes the chances for the second. Drawing a card and keeping it, or taking a sweet from a jar, both work this way: each action alters what is left. The key is that something is removed and not replaced, so the situation for the next event is genuinely different from the first.
Dependent: drawing marbles
Events are dependent when one outcome changes the chances of the next.
A bag holds 3 red and 2 blue. Take one marble out and keep it. What happens to the next chance?
Listing two-step outcomes
When two separate events combine, a grid lists every pairing at once. A coin with two results and a spinner with three gives two times three, which is six combinations, each sitting in one cell of the grid. Organising outcomes this way makes sure none are missed and shows how quickly they multiply as choices grow. This is the systematic listing behind all two-step chance: set out one event along the top, the other down the side, and every combination appears where a row meets a column. A grid turns careful listing into something you can see.
List the combinations
A grid lists every pairing of two separate events.
One coin and one spinner: how many combinations are possible? Fill the grid to see.
Telling the two apart
The central skill of this unit is deciding whether a pair of events is independent or dependent, and there is one clean test: does the first outcome change what is possible for the second? Tossing a coin twice, or rolling a die then spinning a spinner, are independent — nothing is used up, so the second chance is unchanged. Drawing and keeping a card, or taking a sweet, are dependent — something is removed, so the next chance differs. Asking that single question, does the first change the second, sorts almost every everyday chance situation into one of the two kinds.
Independent or dependent?
Decide by asking if the first event changes the chances of the second.
Are these events independent or dependent: tossing a coin, then tossing it again?
Why the difference matters
The difference between independent and dependent events is not just a label; it changes how chance behaves. For independent events, each new event starts fresh, so a coin is fifty-fifty every single time, however many heads came before. For dependent events, the chances shift as things are removed, so each draw must be judged on what is left. Sorting situations into the two kinds, and listing the outcomes of two-step events, gives a child the tools to reason about real chance with two stages — games, draws and choices — and lays the groundwork for calculating combined probabilities in later years, where this distinction becomes essential.
Sorting the events
Independent if separate; dependent if one outcome changes the next.
Each situation is one kind or the other. Reveal each to sort it.
Quick self-check
1. A coin is tossed and lands heads. On the next toss, heads is...
2. You draw a marble from a bag and keep it. The chance for the next draw is...
3. How many possible outcomes are there for tossing two coins?
4. Which of these is a pair of independent events?
5. Taking a sweet from a jar and then taking another is an example of...