Probability | Fourth Grade
Complete Notes & Formulas
1. Understanding Probability
Definition: Probability is the measure of how likely an event is to happen. It tells us the chance or possibility that something will occur.
🎯 What is Probability?
Probability means possibility - it is a way to describe how likely something is to happen.
The probability of an event is always between 0 and 1:
- 0 means the event will NEVER happen (impossible)
- 1 means the event will ALWAYS happen (certain)
- Between 0 and 1 means the event MIGHT happen
📊 Probability Scale (Likelihood of Events):
Term | Meaning | Probability Value |
---|---|---|
Impossible | Will NEVER happen | 0 |
Unlikely | Probably won't happen | Less than ½ |
Equally Likely | 50-50 chance | ½ or 0.5 |
Likely | Probably will happen | More than ½ |
Certain | Will ALWAYS happen | 1 |
✏️ Real-Life Examples:
IMPOSSIBLE (0):
• Rolling a 7 on a standard dice (1-6)
• Getting 2 heads when flipping 1 coin
UNLIKELY (less than ½):
• Rolling a 6 on a dice (1 out of 6 chances)
• Picking a red card from mostly blue cards
EQUALLY LIKELY (½):
• Flipping a coin - heads or tails
• Picking red or blue from equal amounts
LIKELY (more than ½):
• Picking a red card when most cards are red
• Rolling 1, 2, 3, 4, or 5 on a dice (5 out of 6)
CERTAIN (1):
• The sun will rise tomorrow
• Picking a red card when all cards are red
🔑 Key Terms:
- Event: Something that can happen (like flipping a coin)
- Outcome: A possible result (like getting heads)
- Sample Space: All possible outcomes
- Favorable Outcome: The outcome we want
2. Find the Probability
Definition: To find the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes.
📐 Probability Formula:
P(Event) = Number of Favorable Outcomes / Total Number of Possible Outcomes
P(E) = n(A) / n(S)
where n(A) = favorable outcomes, n(S) = total outcomes
📝 Steps to Find Probability:
- Step 1: Count the TOTAL number of possible outcomes
- Step 2: Count the number of FAVORABLE outcomes (what you want)
- Step 3: Divide favorable outcomes by total outcomes
- Step 4: Write as a fraction, decimal, or percentage
✏️ Examples:
Example 1: Rolling a Dice
What is the probability of rolling a 4 on a standard dice?
Solution:
Total possible outcomes = 6 (numbers 1, 2, 3, 4, 5, 6)
Favorable outcomes = 1 (only the number 4)
P(rolling 4) = 1/6
Answer: 1/6
Example 2: Picking from a Bag
A bag has 3 red balls, 2 blue balls, and 5 green balls. What is the probability of picking a green ball?
Solution:
Total balls = 3 + 2 + 5 = 10
Green balls = 5
P(green) = 5/10 = 1/2
Answer: 1/2 or 50%
Example 3: Spinner
A spinner is divided into 8 equal sections: 3 yellow, 2 red, 3 blue. What is the probability of landing on yellow?
Solution:
Total sections = 8
Yellow sections = 3
P(yellow) = 3/8
Answer: 3/8
🔑 Important Rules:
- Probability is always between 0 and 1
- Probability can be written as a fraction, decimal, or percentage
- The sum of all probabilities in an event = 1
- Higher probability = more likely to happen
3. Make Predictions
Definition: Using probability, we can make predictions about what will likely happen in future events. We use known probabilities to estimate expected outcomes.
📐 Prediction Formula:
Expected Outcome = Probability × Number of Trials
This tells us approximately how many times an event will occur
📝 Steps to Make Predictions:
- Step 1: Find the probability of the event
- Step 2: Identify how many times the event will be tried (trials)
- Step 3: Multiply probability by number of trials
- Step 4: Round to nearest whole number if needed
✏️ Examples:
Example 1: Coin Flips
If you flip a coin 100 times, about how many times will it land on heads?
Solution:
P(heads) = 1/2
Number of flips = 100
Expected heads = 1/2 × 100 = 50
Prediction: About 50 heads
Example 2: Drawing Cards
A bag has 2 red and 8 blue marbles. If you pick 30 times (replacing each time), about how many red marbles will you pick?
Solution:
Total marbles = 10
P(red) = 2/10 = 1/5
Number of picks = 30
Expected red = 1/5 × 30 = 6
Prediction: About 6 red marbles
Example 3: Spinner Predictions
A spinner has 4 equal sections: 1 red, 3 blue. If you spin 60 times, about how many times will it land on blue?
Solution:
P(blue) = 3/4
Number of spins = 60
Expected blue = 3/4 × 60 = 45
Prediction: About 45 times blue
💡 Important Notes:
- Predictions are ESTIMATES - actual results may vary slightly
- More trials = predictions closer to actual probability
- Predictions help us understand what to expect
- Real results can be different from predictions
4. Combinations
Definition: A combination is a way of selecting items from a collection where the order doesn't matter. Combinations help us find all possible ways to choose or arrange things.
🎯 What Are Combinations?
Combinations show us all the different ways we can put things together or choose them.
Key Point: In combinations, order doesn't matter
Example: Choosing shirt + pants is the same as choosing pants + shirt
📐 Simple Combination Rules (for Fourth Grade):
Rule 1: Choosing 2 items from different groups
Total Combinations = Number in Group 1 × Number in Group 2
Rule 2: Choosing 3 items from different groups
Total Combinations = Group 1 × Group 2 × Group 3
✏️ Examples:
Example 1: Ice Cream Combinations
An ice cream shop has 3 flavors (vanilla, chocolate, strawberry) and 2 toppings (sprinkles, nuts). How many different combinations are possible?
Solution:
Flavors = 3
Toppings = 2
Total combinations = 3 × 2 = 6
List: Vanilla+Sprinkles, Vanilla+Nuts, Chocolate+Sprinkles, Chocolate+Nuts, Strawberry+Sprinkles, Strawberry+Nuts
Answer: 6 combinations
Example 2: Outfit Combinations
You have 4 shirts and 3 pairs of pants. How many different outfits can you make?
Solution:
Shirts = 4
Pants = 3
Total outfits = 4 × 3 = 12
Answer: 12 different outfits
Example 3: Sandwich Combinations
A sandwich shop has 2 types of bread, 3 types of meat, and 2 types of cheese. How many different sandwich combinations?
Solution:
Bread = 2
Meat = 3
Cheese = 2
Total = 2 × 3 × 2 = 12
Answer: 12 different sandwiches
📝 Finding Combinations with Lists/Trees:
For smaller numbers, you can list all combinations or draw a tree diagram:
- List Method: Write out all possible pairs
- Tree Diagram: Draw branches for each choice
- Multiplication: Multiply the number of options in each group
Probability Quick Reference Chart
Concept | Formula/Rule |
---|---|
Probability | P(E) = Favorable Outcomes / Total Outcomes |
Probability Range | Always between 0 and 1 |
Impossible Event | Probability = 0 |
Certain Event | Probability = 1 |
Equally Likely | Probability = 1/2 or 0.5 |
Making Predictions | Expected = Probability × Trials |
Simple Combinations | Group 1 × Group 2 × Group 3... |
📊 Probability Scale:
Impossible
0
Unlikely
< 1/2
Equal
1/2
Likely
> 1/2
Certain
1
💡 Key Reminders:
- Probability tells us HOW LIKELY something is to happen
- Higher number = MORE likely, Lower number = LESS likely
- Predictions are ESTIMATES based on probability
- Combinations help us count all possible outcomes
📚 Fourth Grade Probability - Complete Study Guide
Master these probability concepts for math excellence! ✨