🎲 Probability - Grade 3
Understanding Probability!
Probability is the chance or likelihood that something will happen! It helps us predict how likely events are!
What You'll Learn:
• How to tell if events are more, less, or equally likely
• How to describe events as certain, probable, unlikely, or impossible
• How to find all possible combinations
📊 More, Less and Equally Likely
What Does "Likely" Mean?
Likely means the chance of something happening! We compare how likely different events are!
Three Types of Likelihood:
1. More Likely
An event is more likely when it has a better chance of happening!
Example: A bag has 7 red marbles and 3 blue marbles.
• Total marbles: 10
• Red marbles: 7
• Blue marbles: 3
Question: Which color is more likely to be picked?
Answer: Red is more likely because there are MORE red marbles! ✓
Why? 7 red > 3 blue
2. Less Likely
An event is less likely when it has a smaller chance of happening!
Example: A spinner has 8 sections:
• 6 yellow sections
• 2 green sections
Question: Which color is less likely to be spun?
Answer: Green is less likely because there are FEWER green sections! ✓
Why? 2 green < 6 yellow
3. Equally Likely
Events are equally likely when they have the SAME chance of happening!
Example 1: Flipping a coin
• Heads: 1 side
• Tails: 1 side
Result: Heads and Tails are equally likely! ✓
Why? Both have the same chance (1 out of 2)
Example 2: A bag has 5 red balls and 5 blue balls.
Red and blue are equally likely to be picked! ✓
Why? 5 red = 5 blue
How to Compare Likelihood:
- Count how many of each item there are
- Compare the numbers
- The one with MORE is more likely
- The one with FEWER is less likely
- If the numbers are EQUAL, they are equally likely
Practice Examples:
Example 1: Fruit Bowl
A bowl has:
• 10 apples 🍎
• 4 bananas 🍌
• 10 oranges 🍊
Questions & Answers:
Q1: Which fruit is less likely to be picked?
A1: Banana (only 4) ✓
Q2: Which two fruits are equally likely?
A2: Apple and Orange (both have 10) ✓
Q3: Is picking a banana more or less likely than picking an apple?
A3: Less likely (4 < 10) ✓
Example 2: Number Cards
Cards numbered: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4
Count:
• Number 1: 1 card
• Number 2: 2 cards
• Number 3: 3 cards
• Number 4: 4 cards
Most likely: Picking 4 (appears most often) ✓
Least likely: Picking 1 (appears least often) ✓
💡 Key Rule: More items = More likely! Fewer items = Less likely!
🎯 Certain, Probable, Unlikely and Impossible
Describing How Likely Events Are:
We use special words to describe the chance of something happening!
Probability Scale:
Impossible → Unlikely → Equally Likely → Likely (Probable) → Certain
The Four Main Terms:
1. IMPOSSIBLE ❌
Impossible means it will NEVER happen! There is NO chance!
Examples of Impossible Events:
• Picking a red marble from a bag with only blue marbles
• Rolling a 7 on a regular 6-sided die (1, 2, 3, 4, 5, 6)
• Flipping a coin and getting a square
• The sun rising in the west
• A dog speaking perfect English
Probability: 0 out of anything = 0 chance!
2. UNLIKELY 🤔
Unlikely means it probably WON'T happen, but it COULD! Small chance!
Examples of Unlikely Events:
• Picking 1 red marble from a bag with 1 red and 9 blue marbles
• It snowing in the summer (in most places)
• Winning the lottery
• Getting all answers right by guessing
Example: A bag has 2 yellow balls and 8 green balls.
Picking yellow is unlikely! (2 out of 10 = small chance)
3. LIKELY (PROBABLE) ✓
Likely or Probable means it will PROBABLY happen! Good chance!
Examples of Likely Events:
• Picking a blue marble from a bag with 9 blue and 1 red marble
• The sun rising tomorrow
• You will go to bed tonight
• It will rain during the rainy season
Example: A spinner has 7 red sections and 1 blue section.
Landing on red is likely! (7 out of 8 = big chance)
4. CERTAIN ✅
Certain means it will DEFINITELY happen! 100% chance!
Examples of Certain Events:
• Picking a blue marble from a bag with ONLY blue marbles
• The sun will set tonight
• You will get older every year
• Water will freeze at 0°C
• Rolling a number between 1 and 6 on a regular die
Probability: All out of all = guaranteed!
Visual Scale:
0% ← Impossible
⬇️
25% ← Unlikely
⬇️
50% ← Equally Likely
⬇️
75% ← Likely (Probable)
⬇️
100% ← Certain
Practice Problems:
Problem Set:
Describe each event as: Impossible, Unlikely, Likely, or Certain
1. You will breathe air today.
Answer: CERTAIN ✓
2. You will fly to Mars tomorrow.
Answer: IMPOSSIBLE ✓
3. It will rain at some point this year.
Answer: LIKELY ✓
4. You will meet a real dinosaur.
Answer: IMPOSSIBLE ✓
5. You will eat dessert every day this week.
Answer: UNLIKELY (depends, but not guaranteed) ✓
💡 Remember: If it can't happen = Impossible! If it must happen = Certain!
🔀 Combinations
What are Combinations?
Combinations are all the different ways we can put things together! The order doesn't matter in combinations!
For example: If you have a shirt and pants, how many different outfits can you make?
Basic Counting Principle:
Total Combinations =
\(\text{Number of First Choices} \times \text{Number of Second Choices}\)
How to Find All Combinations:
- List all items in the first group
- List all items in the second group
- Match each item from the first group with every item from the second group
- Count all the combinations
Examples:
Example 1: Ice Cream Combinations
Problem: An ice cream shop has:
• 2 flavors: Chocolate, Vanilla
• 3 toppings: Sprinkles, Nuts, Cherries
How many different ice cream combinations can you make?
Method 1: List all combinations
Chocolate with:
1. Chocolate + Sprinkles
2. Chocolate + Nuts
3. Chocolate + Cherries
Vanilla with:
4. Vanilla + Sprinkles
5. Vanilla + Nuts
6. Vanilla + Cherries
Total: 6 combinations! ✓
Method 2: Use multiplication
\(2 \text{ flavors} \times 3 \text{ toppings} = 6 \text{ combinations}\) ✓
Example 2: Outfit Combinations
Problem: You have:
• 3 shirts: Red, Blue, Green
• 2 pants: Jeans, Shorts
How many different outfits can you make?
List all outfits:
1. Red shirt + Jeans
2. Red shirt + Shorts
3. Blue shirt + Jeans
4. Blue shirt + Shorts
5. Green shirt + Jeans
6. Green shirt + Shorts
Total: 6 outfits! ✓
Quick way: \(3 \times 2 = 6\) ✓
Example 3: Lunch Combinations
Problem: School lunch menu has:
• 2 main dishes: Pizza, Burger
• 2 sides: Salad, Fries
• 2 drinks: Milk, Juice
How many different lunch combinations are possible?
Using multiplication:
\(2 \text{ mains} \times 2 \text{ sides} \times 2 \text{ drinks}\)
\(= 2 \times 2 \times 2 = 8\) combinations ✓
List all 8 combinations:
1. Pizza + Salad + Milk
2. Pizza + Salad + Juice
3. Pizza + Fries + Milk
4. Pizza + Fries + Juice
5. Burger + Salad + Milk
6. Burger + Salad + Juice
7. Burger + Fries + Milk
8. Burger + Fries + Juice ✓
Example 4: Coin and Die
Problem: You flip a coin and roll a die.
• Coin: 2 outcomes (Heads, Tails)
• Die: 6 outcomes (1, 2, 3, 4, 5, 6)
How many different combinations?
Calculate:
\(2 \times 6 = 12\) combinations ✓
All combinations:
Heads-1, Heads-2, Heads-3, Heads-4, Heads-5, Heads-6
Tails-1, Tails-2, Tails-3, Tails-4, Tails-5, Tails-6
Using a Tree Diagram:
A tree diagram helps us see all combinations visually!
Example: 2 shirts (A, B) and 2 pants (X, Y)
Tree Diagram:
Start
↙ ↘
A B
↙ ↘ ↙ ↘
X Y X Y
Combinations: AX, AY, BX, BY = 4 total ✓
💡 Quick Tip: Multiply the number of choices to find total combinations!
📝 Important Probability Formulas
Comparing Likelihood:
More Likely: More items = Better chance
Less Likely: Fewer items = Smaller chance
Equally Likely: Same number = Same chance
Probability Terms:
Impossible: 0% chance (will never happen)
Unlikely: Small chance (probably won't happen)
Likely: Big chance (probably will happen)
Certain: 100% chance (will definitely happen)
Combinations Formula:
For 2 groups:
\(\text{Total Combinations} = \text{Group 1} \times \text{Group 2}\)
For 3 groups:
\(\text{Total} = \text{Group 1} \times \text{Group 2} \times \text{Group 3}\)
Quick Reference Table:
| Term | Meaning | Example |
|---|---|---|
| Impossible | Cannot happen | Rolling a 7 on a regular die |
| Unlikely | Probably won't happen | Picking 1 red from 9 blue marbles |
| Likely | Probably will happen | Picking 9 red from 1 blue marble |
| Certain | Will definitely happen | Picking blue from all blue marbles |
💡 Quick Learning Tips
- ✓ More items = More likely to pick that item!
- ✓ Fewer items = Less likely to pick that item!
- ✓ Same number of items = Equally likely!
- ✓ Impossible = 0% chance (never happens)
- ✓ Certain = 100% chance (always happens)
- ✓ Unlikely = small chance but possible
- ✓ Likely = big chance, probably happens
- ✓ To find combinations: multiply the number of choices!
- ✓ Tree diagrams help you see all combinations
- ✓ List all combinations to make sure you don't miss any
- ✓ Probability is about predicting the future!
- ✓ Count carefully when comparing likelihood
- ✓ Use real-life examples: coins, dice, spinners, marbles
- ✓ Order doesn't matter in combinations
- ✓ Practice with everyday choices (outfits, food, games)