Basic Math

Probability | Fourth Grade

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):

TermMeaningProbability Value
ImpossibleWill NEVER happen0
UnlikelyProbably won't happenLess than ½
Equally Likely50-50 chance½ or 0.5
LikelyProbably will happenMore than ½
CertainWill ALWAYS happen1

✏️ 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:

  1. Step 1: Count the TOTAL number of possible outcomes
  2. Step 2: Count the number of FAVORABLE outcomes (what you want)
  3. Step 3: Divide favorable outcomes by total outcomes
  4. 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:

  1. Step 1: Find the probability of the event
  2. Step 2: Identify how many times the event will be tried (trials)
  3. Step 3: Multiply probability by number of trials
  4. 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

ConceptFormula/Rule
ProbabilityP(E) = Favorable Outcomes / Total Outcomes
Probability RangeAlways between 0 and 1
Impossible EventProbability = 0
Certain EventProbability = 1
Equally LikelyProbability = 1/2 or 0.5
Making PredictionsExpected = Probability × Trials
Simple CombinationsGroup 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! ✨

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