MathIsimple

Lesson 5-3: Basic Probability

Understand probability concepts and calculate simple probabilities using game night scenarios!

Learning Scenario: Game Night

Scenario: You're hosting a game night with friends and want to play some games that involve chance. You have a standard 6-sided die, a coin, and a bag with 4 red marbles and 6 blue marbles. What are the chances of rolling a 3, flipping heads, or picking a red marble?

What We Need to Find:

  • • Probability of rolling a 3 on a die
  • • Probability of flipping heads on a coin
  • • Probability of picking a red marble
  • • How to express probability as fractions and percentages

Tools We'll Use:

  • • Counting possible outcomes
  • • Calculating favorable outcomes
  • • Probability formulas
  • • Fractions and percentages

Understanding Probability

What is Probability?

Probability is a way to measure how likely something is to happen. It tells us the chance that a particular event will occur. We express probability as a number between 0 and 1, or as a fraction, decimal, or percentage.

Probability = Favorable Outcomes ÷ Total Outcomes

The chance something will happen

Probability Scale:

0 = Impossible, 0.5 = 50/50 chance, 1 = Certain

Real Examples:

Weather forecasts, game outcomes, medical tests

Rolling a Die

Probability of Rolling a 3

Let's find the probability of rolling a 3 on a standard 6-sided die:

Total possible outcomes: 6 (1, 2, 3, 4, 5, 6)

All the numbers on the die

Favorable outcomes: 1 (just the number 3)

The outcome we want

Probability = 1 ÷ 6 = 1/6

Calculate the probability

Answer: 1/6 or about 16.7%

The chance of rolling a 3

Flipping a Coin

Probability of Flipping Heads

Let's find the probability of flipping heads on a fair coin:

Total possible outcomes: 2 (Heads, Tails)

Only two sides on a coin

Favorable outcomes: 1 (Heads)

The outcome we want

Probability = 1 ÷ 2 = 1/2

Calculate the probability

Answer: 1/2 or 50%

Equal chance of heads or tails

Picking Marbles

Probability of Picking a Red Marble

Let's find the probability of picking a red marble from a bag with 4 red marbles and 6 blue marbles:

Total marbles: 4 red + 6 blue = 10 marbles

All marbles in the bag

Red marbles: 4

The marbles we want

Probability = 4 ÷ 10 = 4/10 = 2/5

Calculate and simplify

Answer: 2/5 or 40%

The chance of picking red

More Probability Examples

Common Probability Situations

Rolling an even number on a die

3/6 = 1/2 = 50%

Drawing a heart from a deck of cards

13/52 = 1/4 = 25%

Picking a blue marble (from our bag)

6/10 = 3/5 = 60%

Rolling a number greater than 4

2/6 = 1/3 ≈ 33%

Practice Problems

Problem 1: Spinner Game

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

Total sections: 8

All sections on the spinner

Red sections: 3

Sections we want

Probability = 3/8 = 37.5%

Calculate the probability

Answer: 3/8 or 37.5%

Problem 2: Card Game

From a standard deck of 52 cards, what is the probability of drawing a king?

Total cards: 52

All cards in the deck

Kings: 4 (one in each suit)

Cards we want

Probability = 4/52 = 1/13 ≈ 7.7%

Calculate and simplify

Answer: 1/13 or about 7.7%

Real-World Applications

Where We Use Probability

Games & Entertainment

  • • Board games and card games
  • • Sports statistics and predictions
  • • Lottery and gambling odds
  • • Video game mechanics

Science & Medicine

  • • Weather forecasting
  • • Medical test results
  • • Drug effectiveness studies
  • • Genetic inheritance

Key Takeaways

Probability Basics

  • Probability measures how likely something is to happen
  • Formula: Favorable Outcomes ÷ Total Outcomes
  • Probability is always between 0 and 1
  • Can be expressed as fractions, decimals, or percentages

Common Examples

  • Coin flip: 1/2 or 50% chance
  • Die roll: 1/6 chance for any specific number
  • Marbles: Count favorable vs. total marbles
  • Cards: 4/52 = 1/13 chance for any specific card