L1 · Sample Spaces and Set Notation

Learning goal

“I can write the sample space of an experiment - including compound experiments with two events - using set notation, a systematic list, a table, or a tree, and I can tell whether two events are independent or dependent.”

Sample space — the set of ALL possible outcomes of an experiment. If an outcome is possible but missing from the list, the sample space is wrong.

Set notation — writing a set inside braces: the sample space for flipping a coin is S = {H, T}. The letter S names the sample space.

Compound event — an event made of two or more events happening together, like flipping a coin AND rolling a die. Its outcomes are ordered pairs such as (H, 4).

Outcome — one possible result of an experiment. In a compound event, one outcome is one complete pair (or triple), not one part of it.

Worked example

Write the sample space for rolling a six-sided die, using set notation. Step 1: List every possible outcome: 1, 2, 3, 4, 5, 6. Not the outcome you HOPE for, not the last outcome you saw - every outcome the die can produce. Step 2: Put the list in braces and name it: S = {1, 2, 3, 4, 5, 6}. Step 3: Sanity-check the set: 0 is not in S (a die has no 0 face); 7 is not in S. Every face is in, nothing else is in. Say it plainly: the sample space is a promise - "these are ALL the things that can happen, and nothing else can." Set notation is just the tidy way to write that promise.

Check yourself — explain it

Why is S = {1, 2, 3, 4, 5} wrong for a die roll, even though the die landed on 5 last time?

Paired problem — example still visible

A spinner has 4 equal sections labelled A, B, C, D. Write its sample space in set notation. -> S = {A, B, C, D}

Faded completion — last step is yours

"For flipping a coin, S = {H, ___.}" -> T

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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