Lesson 6-3: Probability Calculations

Understand probability concepts and calculate the likelihood of events using fractions and percentages.

Probability

Fractions

Chance

Likelihood

What You'll Learn

• Understand what probability means and how to express it
• Calculate probability using fractions and percentages
• Compare probabilities of different events
• Use probability to make predictions
• Apply probability to real-world situations

What is Probability?

Understanding Probability

Probability tells us how likely something is to happen. It's expressed as a number between 0 and 1, or as a fraction, decimal, or percentage.

Probability Scale:

• 0 = Impossible (will never happen)

• 0.5 or 1/2 = Equally likely (50% chance)

• 1 = Certain (will always happen)

• 0.25 or 1/4 = Unlikely (25% chance)

• 0.75 or 3/4 = Likely (75% chance)

Basic Formula:

Probability = Favorable outcomes ÷ Total possible outcomes

Key Terms:

Outcome: A possible result of an experiment
Favorable outcome: The outcome you're interested in
Total outcomes: All possible results
Event: Something that might happen

Simple Probability Examples

Example 1: Rolling a Die

Question: What's the probability of rolling a 3 on a standard die?

Step 1: Count total possible outcomes: 6 (1, 2, 3, 4, 5, 6)

Step 2: Count favorable outcomes: 1 (just the 3)

Step 3: Calculate: 1 ÷ 6 = 1/6

Answer: The probability is 1/6 or about 16.7%

Example 2: Drawing from a Bag

Question: A bag contains 4 red marbles, 3 blue marbles, and 2 green marbles. What's the probability of drawing a red marble?

Step 1: Count total marbles: 4 + 3 + 2 = 9 marbles

Step 2: Count red marbles: 4 marbles

Step 3: Calculate: 4 ÷ 9 = 4/9

Answer: The probability is 4/9 or about 44.4%

Example 3: Flipping a Coin

Question: What's the probability of getting heads when flipping a coin?

Step 1: Count total outcomes: 2 (heads, tails)

Step 2: Count favorable outcomes: 1 (heads)

Step 3: Calculate: 1 ÷ 2 = 1/2

Answer: The probability is 1/2 or 50%

Practice Problem

Question: A spinner has 8 equal sections: 3 red, 2 blue, 2 green, and 1 yellow. What's the probability of landing on blue?

Your calculation:

Comparing Probabilities

Which Event is More Likely?

When comparing probabilities, convert them to the same format (fractions, decimals, or percentages) to make accurate comparisons.

Example: Comparing Events

Event A: Rolling an even number on a die (2, 4, or 6)
Event B: Rolling a number greater than 4 (5 or 6)

Event A: 3 favorable outcomes ÷ 6 total = 3/6 = 1/2 = 50%

Event B: 2 favorable outcomes ÷ 6 total = 2/6 = 1/3 ≈ 33.3%

Conclusion: Event A is more likely than Event B

Probability Comparison Rules:

Higher numerator = more likely (if denominators are the same)
Convert to decimals to compare easily
Use percentages for real-world understanding
Remember: 1/2 = 0.5 = 50%

Practice Problem

Question: A bag has 5 red balls, 3 blue balls, and 2 green balls. Which is more likely: drawing a red ball or drawing a blue ball?

Your comparison:

Real-World Applications

Everyday Probability

• Weather forecasts (70% chance of rain)
• Sports statistics (batting averages)
• Game strategies (card games, board games)
• Medical tests (accuracy rates)
• Insurance calculations

Making Decisions

• Choosing the best route to school
• Deciding which game to play
• Understanding risk vs. reward
• Planning for different outcomes
• Setting realistic expectations

Example: Weather Decision

If there's a 30% chance of rain, should you bring an umbrella?

• 30% chance of rain = 3/10 probability

• 70% chance of no rain = 7/10 probability

• Decision: It's more likely to NOT rain, but bringing an umbrella is a small cost for protection

Practice Problems

Problem 1: Basic Probability

A deck of cards has 52 cards: 13 hearts, 13 diamonds, 13 clubs, and 13 spades. What's the probability of drawing a heart?

Your answer:

Problem 2: Multiple Events

A box contains 6 red pencils, 4 blue pencils, and 2 green pencils. What's the probability of drawing a red or blue pencil?

Your calculation:

Problem 3: Probability Comparison

A spinner has 12 equal sections: 4 red, 3 blue, 3 green, and 2 yellow.

Questions:

What's the probability of landing on red?
What's the probability of landing on yellow?
Which color is most likely to be landed on?
Which color is least likely to be landed on?

Problem 4: Real-World Application

A school cafeteria offers 3 main dishes, 4 side dishes, and 2 desserts. If you randomly choose one item from each category, what's the probability of getting your favorite main dish, side dish, and dessert?

Your solution:

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