Listing Possible Outcomes
Outcomes of Rolling a Die
A standard die has 6 faces. Count the dots.
Possible or Impossible? (A)
Circle POSSIBLE or IMPOSSIBLE.
Rolling a 7 on a standard die
Flipping heads on a coin
Drawing red from a bag with only blue and green
Rolling an even number on a standard die
Possible or Impossible? (B)
Circle POSSIBLE or IMPOSSIBLE.
A baby being born on a Tuesday
Rolling 0 on a standard die
Picking a red marble from a bag of red marbles
Flipping a coin and getting neither heads nor tails
List All Outcomes (A)
Write all possible outcomes.
Flipping a coin: ___
Rolling a standard die: ___
Choosing from red, blue, green and yellow marbles: ___
Spinning a spinner with sections 1, 2, 3, 4: ___
List All Outcomes (B)
Write all possible outcomes.
Days of the week: ___
Months that start with J: ___
Even numbers on a die: ___
Outcomes when picking a card that is red or black: ___
Sort: How Many Outcomes?
Sort each experiment by the number of possible outcomes.
Match Experiments to Outcome Counts
Draw a line from each experiment to how many outcomes it has.
Outcome Counting
Total outcomes = outcomes of event 1 × outcomes of event 2.
Counting Outcomes
Circle the correct number of outcomes.
Flipping a coin has ___ outcomes.
Rolling a die has ___ outcomes.
Picking a card suit has ___ outcomes.
A spinner with 5 equal sections has ___ outcomes.
How Many Outcomes? (A)
Count the total number of possible outcomes.
Flipping two coins (list all combinations): ___. Total: ___
Rolling a die and flipping a coin — how many combined outcomes? ___
How Many Outcomes? (B)
Count the outcomes.
Two spinners, each with 3 sections. Total outcomes: ___
Rolling two dice. Total outcomes: ___
Flipping 3 coins. Total outcomes: ___. List them all:
Systematic Listing (A)
List ALL possible outcomes systematically.
Choose one top (red or blue) and one bottom (shorts or pants). List all outfits:
A lunch menu: sandwich (ham or cheese) and drink (juice, milk or water). List all meals:
Systematic Listing (B)
List all outcomes systematically.
A pizza with 3 base choices (thin, thick, stuffed) and 2 toppings (cheese, pepperoni). List all pizzas:
A gift bag colour (red, blue, green) with a ribbon (gold, silver). List all combinations:
Tree Diagrams (A)
Use a tree diagram to list outcomes.
Flip a coin twice. Draw a tree diagram showing all outcomes (HH, HT, TH, TT).
How many outcomes total? ___ How many have at least one head? ___
Tree Diagrams (B)
Draw a tree diagram.
You choose a main (burger or wrap) and a side (chips, salad or fruit). Draw the tree diagram.
How many meal combinations? ___
Combined Outcomes
Circle the correct total outcomes.
2 coins flipped: ___ outcomes
A die and a coin: ___ outcomes
3 coins flipped: ___ outcomes
2 dice rolled: ___ outcomes
Systematic Listing Challenge
List outcomes for these complex experiments.
A 3-digit code using digits 1, 2, 3 (digits can repeat). How many codes? List the first 10:
Choosing 2 items from {A, B, C, D} where order does not matter. List all combinations:
Outcome Word Problems (A)
Solve these problems.
An ice cream shop has 4 flavours and 3 toppings. How many different single-scoop sundaes?
A password is 2 letters from {A, B, C}. How many passwords if letters can repeat? ___. If they cannot repeat? ___
Outcome Word Problems (B)
Solve these.
You have 5 T-shirts and 3 pairs of shorts. How many different outfits?
A car comes in 4 colours and 2 types (sedan, SUV). How many options?
A class has 3 boys and 4 girls. How many ways to pick one boy and one girl?
Create Your Own Listing Problem
Write your own problem about listing outcomes.
Write a problem about combinations (e.g., meals, outfits, codes). Then list all outcomes.
Possible or Impossible? (C)
Circle POSSIBLE or IMPOSSIBLE.
Drawing a green marble from a bag with only green marbles
Rolling a negative number on a standard die
Getting a number less than 7 on a standard die
Picking a weekend day randomly and getting Monday
Possible or Impossible? (D)
Circle POSSIBLE or IMPOSSIBLE.
Flipping a coin and getting heads three times in a row
Rolling two dice and getting a total of 13
Picking an even number from {2, 4, 6, 8}
Drawing a striped marble from a bag of solid-colour marbles
List All Outcomes (C)
Write all possible outcomes.
Spinning a spinner with sections: A, B, C, D, E: ___
Picking a vowel from the English alphabet: ___
Rolling a number less than 4 on a die: ___
Choosing heads or tails on 1 coin, then even or odd on a die: ___
List All Outcomes (D)
Write all possible outcomes.
Picking a month that starts with J: ___
Rolling a prime number on a die: ___
Choosing a day that is on the weekend: ___
Picking a single digit even number: ___
Sort: How Many Outcomes? (B)
Sort each experiment.
Match Experiments to Outcome Counts (B)
Draw a line.
Outcome Counting (B)
Total outcomes = event 1 outcomes × event 2 outcomes.
How Many Outcomes? (C)
Count the total outcomes.
3 shirts × 4 pants = ___ outfits
A coin and a spinner with 5 sections: ___ outcomes
Two dice: ___ × ___ = ___ outcomes
4 coins flipped: ___ outcomes. (Hint: 2 × 2 × 2 × 2)
Systematic Listing (C)
List ALL outcomes systematically.
You choose a drink (hot chocolate, tea) and a biscuit (plain, chocolate, oat). List all snack combinations:
A car can be red, blue or white, and manual or automatic. List all combinations:
Systematic Listing (D)
List outcomes systematically.
A 2-digit number using only digits 1, 2 and 3 (repeats allowed). List all: ___
How many numbers did you list? ___ Does this match 3 × 3? ___
Tree Diagrams (C)
Use a tree diagram.
A coin is flipped and then a spinner with sections (1, 2, 3) is spun. Draw the tree diagram.
How many outcomes? ___ List 3 of them: ___
Combined Outcomes (B)
Circle the correct total.
A spinner (3 sections) and a die: ___ outcomes
A coin and a spinner (4 sections): ___ outcomes
Three coins: ___ outcomes
Two spinners, each with 4 sections: ___ outcomes
Use a Table to List Outcomes
Use a grid/table to list all outcomes.
Coin (H, T) × Die (1-6): draw a table and fill in all 12 outcomes.
How many outcomes have heads AND an even number? ___
Match Experiments to Methods
Draw a line from each experiment to the best method for listing.
Systematic Listing Challenge (B)
List outcomes for complex experiments.
A padlock has 3 digits, each 0-9. How many possible codes? ___. Why can't you list them all?
Choosing 2 items from {A, B, C, D, E} where order matters. How many arrangements? List them:
Outcome Word Problems (C)
Solve these.
A pizza has 3 sizes, 2 crusts and 5 toppings. How many single-topping pizzas? ___
You have 4 hats and 3 scarves. How many hat-scarf combinations? ___
A number plate has 3 letters then 3 digits. How many plates are possible? (26 letters, 10 digits)
Outcome Word Problems (D)
Solve these.
A restaurant offers 3 entrees, 5 mains and 4 desserts. How many different 3-course meals? ___
A class has 10 boys and 12 girls. How many ways to pick one boy and one girl for a project? ___
You flip a coin 5 times. How many possible sequences of H and T? ___
Counting Principle
Circle the correct answer.
The counting principle says we ___ the number of options for each choice.
3 choices then 4 choices = ___ total outcomes
5 × 5 × 5 = ___ outcomes for a 3-digit code using 5 symbols
2 × 3 × 4 = ___ outcomes for 3 sequential choices
Create and Solve Listing Problems
Write and solve your own problems.
Write a problem about outfit combinations. Solve it.
Write a problem about menu choices. Solve it.
Match Experiments to Outcome Counts (C)
Draw a line.
Outcome Counting (C)
Total outcomes = event 1 × event 2 × event 3.
Possible or Impossible? (E)
Circle POSSIBLE or IMPOSSIBLE.
Drawing the number 7 from a set of cards numbered 1-6
Rolling an odd number on a standard die
Spinning blue on a spinner that is all red
Getting a total of 12 when rolling two dice
Sort: How Many Outcomes? (C)
Sort each experiment by outcome count.
How Many Outcomes? (D)
Use the counting principle.
A password is one letter (A-Z) and one digit (0-9). Total passwords: ___
Choose breakfast (3 options) and lunch (5 options): total meal plans: ___
6 shirts × 5 trousers × 4 ties: total outfits: ___
Roll a die and spin a spinner with 8 sections: total outcomes: ___
Systematic Listing (E)
List all outcomes systematically.
Toss two coins. List all outcomes. Hint: start with HH.
Toss a coin and roll a die showing only 1, 2, 3. List all outcomes:
How many outcomes in each? Coins: ___ Coin+die: ___
Tree Diagrams (D)
Draw tree diagrams.
Choose a colour (red, blue) then a number (1, 2, 3). Draw the tree diagram showing all 6 outcomes.
What is the total number of outcomes? ___ List 3 of them: ___
Outcomes in a Game
A game tracks outcomes each round.
| Win | |
| Draw | |
| Lose |
How many possible outcomes are there?
How many rounds were played?
What fraction of rounds were wins?
Was any outcome more common than expected?
Favourite Choice from 4 Options
Students chose from 4 options. Count results.
| Item | Tally | Total |
|---|---|---|
Option A | ||
Option B | ||
Option C | ||
Option D |
Outcome Tables
Complete the outcome tables.
Fill in a table showing all outcomes for rolling two dice (1-3 only). Rows: die 1. Columns: die 2. Total outcomes: ___
How many outcomes give a total of 4? ___. How many give a total of 6? ___
Counting Principle (B)
Circle the correct total.
5 shirts × 3 pants = ___ outfits
2 choices then 3 choices then 4 choices = ___
A 4-digit PIN using digits 0-9 has ___ possible combinations.
If there are 3 colours and 4 sizes, how many ways to pick one of each?
Outcome Word Problems (E)
Solve these.
A test has 5 true/false questions. How many different answer sequences are possible?
A sandwich can have 2 bread types, 4 fillings and 3 sauces. How many sandwiches?
A class has 12 students. How many ways to pick a leader and deputy (order matters)?
Permutations Introduction
How many ways to arrange items in order?
Arrange 3 books (A, B, C) on a shelf. List all arrangements: ___. Total: ___
Arrange just 2 of the 3 books. How many ways? ___
Match Listing Method to Situation
Draw a line.
Outcome Counting (D)
Total = choice 1 × choice 2 × choice 3. Find the missing factor.
Possible or Impossible? (F)
Circle POSSIBLE or IMPOSSIBLE.
Getting a total of 1 when rolling two standard dice
Flipping exactly 3 heads in 3 coin tosses
Picking both red and blue at the same time from a bag
Getting a total of 12 when rolling two dice
Sort: Small or Large Sample Space?
Sort each experiment.
List Outcomes Using a Grid (B)
Use a table to list all outcomes.
Flip a coin and spin a 3-colour spinner. Make a table showing all outcomes:
Total outcomes: ___. How many include Heads? ___. How many include Red? ___
Systematic Listing (F)
List all combinations.
Ice cream: vanilla (V) or chocolate (C), with sprinkles (S), nuts (N) or sauce (A). List all 6 combos:
Which listing method did you use? ___
Counting Without Listing
Use the counting principle — don't list all outcomes.
A phone screen lock has 4 digits, each from 0-9. How many different codes? ___
If the same digit cannot be repeated, how many codes? (10 × 9 × 8 × 7) ___
Why would listing all codes be impractical? ___
Event Possibility Discussion
Discuss event possibility.
Can rolling a die and flipping a coin both result in ONLY even numbers? ___
If you roll two dice, is it possible to get the same total in two different ways? Explain.
How many ways can you roll a total of 7 with two dice? List them:
Ice Cream Combination Choices
Students chose their favourite combination.
| V + Sprinkles | |
| V + Sauce | |
| C + Sprinkles | |
| C + Sauce |
Most popular combination?
How many combinations were possible?
Were all combinations equally popular?
Total students surveyed?
Dice Roll Combinations
Results of rolling two dice and recording each outcome pair.
| Item | Tally | Total |
|---|---|---|
Both same | ||
Sum < 7 | ||
Sum = 7 | ||
Sum > 7 |
Apply the Counting Principle
Use multiplication to count outcomes.
A bike can be red, blue or green. It can have 5-speed or 10-speed gears. How many combinations? ___
A restaurant has 4 entrees, 8 mains and 5 desserts. How many 3-course meal options? ___
You can choose 1 of 3 activities each morning and 1 of 4 each afternoon for 5 days. How many different weekly plans? ___
Sample Space for Card Games
Explore a standard 52-card deck.
How many outcomes when picking 1 card? ___
List all possible suits: ___
If you pick one card, how many outcomes are hearts? ___ Face cards? ___ Red cards? ___
How many outcomes when picking 2 cards in order (without replacement)? ___
Match Listing Method to Situation
Draw a line.
Counting Principle (B)
Event A has a outcomes. Event B has b outcomes. Total = a × b. Find the missing value.
Correct Outcome Count (B)
Circle the correct number of outcomes.
2 coins tossed
1 die rolled + 1 coin tossed
3 coins tossed
Choose 1 of 4 drinks AND 1 of 3 snacks
Sort Outcomes: Possible or Impossible?
Sort each event.
Tree Diagram for Three Events
Draw a tree diagram.
You choose a sport (soccer or tennis), then a snack (apple or banana), then a drink (water or juice). Draw the tree diagram:
How many outcomes? ___
List all outcomes that include tennis:
Two-Way Table Outcomes
Complete the two-way table.
A die (1–6) is rolled. A coin is flipped (H/T). Create the two-way table (6 rows × 2 columns):
Total outcomes: ___. How many show an even number AND heads? ___
Exponential Outcome Sequences
These show how outcomes multiply. Continue.
Compare Outcome Spaces
Tick which has more outcomes.
Tossing 2 coins (4 outcomes) vs rolling 1 die (6 outcomes)
1 die + 1 coin (12 outcomes) vs tossing 3 coins (8 outcomes)
Outcomes in Games (B)
Analyse game outcomes.
A card game uses a deck of 10 cards (1–10). Player wins if they draw 3 or higher. How many winning outcomes? ___. How many losing? ___
A game has two spinners: one with 3 sections, one with 4 sections. Total game outcomes: ___
Which is a fairer game: a 50% chance or a 1-in-3 chance? Explain:
Complementary Outcomes
Use complementary counting.
A bag has 10 balls: 3 red, 4 blue, 3 green. How many outcomes are NOT red? ___
A die is rolled. How many outcomes are NOT a 6? ___. Not a prime number? ___
Why is it sometimes easier to count 'not' outcomes?
Real-Life Sample Spaces
Explore sample spaces in real life.
A restaurant menu has 3 starters, 5 mains, 4 desserts. How many 3-course combinations? ___
A student can choose 4 electives from 8 options. Is this a sample space problem? Why?
Where else in real life do people need to count possible outcomes?
Venn Diagram for Compound Events
Use a Venn diagram to show outcomes.
A die is rolled. Event A: odd number. Event B: greater than 3. List all outcomes: ___
Draw a Venn diagram showing A only, B only, and A AND B (both):
How many outcomes are in A OR B (either or both)? ___
Systematic Listing: Full Method
Use a systematic method to list all outcomes.
You toss 3 coins. Use systematic listing (start with all Heads): ___, ___, ___...
How many outcomes total? ___ How many have exactly 2 heads? ___
Compare with the counting principle: 2 × 2 × 2 = ___
Event Probability from Sample Space
Use the sample space to calculate probability.
Two dice are rolled. Total outcomes: ___. P(sum = 7) = ___
P(both dice show the same number) = ___
P(at least one 6) = ___ (Hint: count outcomes with at least one 6)
Pascal's Triangle and Outcomes
Pascal's Triangle shows combinations.
Row 1: 1. Row 2: 1 1. Row 3: 1 2 1. Row 4: 1 3 3 1. Row 5: ___
The numbers in row 4 (1 3 3 1) show outcomes for 3 coin tosses: 0 heads, 1 head, 2 heads, 3 heads. How many ways to get 2 heads? ___
Using row 5, how many ways to get exactly 2 heads in 4 coin tosses? ___
Probability Listing Method to Situation (B)
Match each method to its best situation.
Counting Outcomes (B)
Use the counting principle.
Total Number of Outcomes (C)
Circle the correct number of outcomes.
4 shirts and 3 pants combinations:
2 coins tossed together:
1 die rolled and 1 coin tossed:
3 choices of main and 2 of dessert:
Sort: How Many Outcomes? (Least to Most)
Sort each experiment by number of outcomes.
Tree Diagram: 3-Step Event
Draw a tree diagram for 3 choices.
A meal: starter (soup/salad), main (pasta/chicken), dessert (ice cream/cake). Draw the tree diagram:
How many meal combinations? ___. How many include both soup and cake? ___
Organised List for Complex Outcomes
Use an organised list to count outcomes.
You choose 2 letters from {A, B, C, D} without repeating. List all ordered pairs: ___
Total ordered pairs: ___. If order doesn't matter, total: ___
Counting Outcomes Sequences
Continue the sequence of total outcomes.
Compare Outcome Counts (B)
Which has more outcomes?
1 die (6 outcomes) vs tossing 3 coins (8 outcomes)
Two 6-sided dice (36) vs two 4-sided dice (16) — which has more?
Types of Outcomes Students Listed
Tally how many students listed each type correctly.
| Item | Tally | Total |
|---|---|---|
Simple (1 event) | ||
Two events combined | ||
Three events combined | ||
Compound with replacement |
Spinner Outcomes
A spinner has sections: 1, 1, 2, 3, 3, 3. Each icon = 10 spins.
| Number 1 | |
| Number 2 | |
| Number 3 |
Total spins recorded?
Which number appeared most?
Expected probability of 1: ___. Experimental: ___
Expected probability of 3: ___. Experimental: ___
Two-Way Tables as Sample Spaces
A two-way table shows all outcomes for two events.
Spinner 1: Red or Blue. Spinner 2: 1, 2, or 3. Draw the two-way table showing all 6 outcomes:
P(Red AND 2) = ___. P(Blue AND odd number) = ___
Counting Principle in Planning
Use multiplication to count options.
A school uniform: 3 colours × 2 styles × 2 sizes = ___ combinations
A password with 2 letters (A-E) then 2 digits (0-9): ___ possible passwords
If you add a third digit to the password, how many new combinations? ___
Listing Method: Which is Most Efficient?
Choose the most efficient method.
For 2 coin tosses (4 outcomes), the best method is:
For 3 dice (216 outcomes), the best method is:
For checking P(specific outcome), you need:
For 5 binary choices, outcomes = 2^5 =
Sample Space: Card Drawing
A deck has 4 suits (Hearts, Diamonds, Clubs, Spades) and cards 1–5.
Total cards: ___. List all Heart cards: ___
P(drawing a red 3) = ___. P(drawing any 4) = ___. P(drawing a Club or Spade 1) = ___
P(drawing a face card) if face cards are J, Q, K = ___. (There are none in this mini-deck)
Home Activity: Chance Experiments
Try these at home!
- 1Flip a coin 20 times. Record outcomes. How many heads and tails?
- 2Put 5 different coloured socks in a bag. List the outcomes before picking one.
- 3Make a spinner with 4 sections. Predict outcomes, then spin 20 times.
- 4Choose 3 toppings for a sandwich from 5 options. How many combinations?