Introduction to Probability — What Is Probability, Sample Space & Events

1. What is Probability?

Probability is a way to measure how likely something is to happen. We use it every day without even thinking about it!

Key Idea: Probability is a number between 0 and 1 that tells us the chance of something happening.

0 means impossible (will never happen)
1 means certain (will definitely happen)
0.5 (or 50%) means equally likely to happen or not happen

Example: Flipping a Coin

When you flip a fair coin, there are two possible outcomes:

The probability of getting heads = 1/2 = 0.5 = 50%

The probability of getting tails = 1/2 = 0.5 = 50%

Practice Question 1

The weather forecast says there's a 70% chance of rain tomorrow. What is this probability as a decimal?

2. Random Experiments and Outcomes

A random experiment is an action where we can't predict the exact result, but we know all possible results.

Sample Space

The sample space is the set of all possible outcomes of an experiment. We often use the symbol S or Ω (omega).

Example: Rolling a Die

When you roll a standard six-sided die:

Sample Space S = {1, 2, 3, 4, 5, 6}

Each outcome has probability = 1/6 ≈ 0.167 ≈ 16.7%

Practice Question 2

You have a bag with 3 red balls and 2 blue balls. If you pick one ball randomly, what is the sample space?

3. Events

An event is a collection of one or more outcomes from the sample space. Events are what we calculate probabilities for!

Example: Events with Dice

Consider rolling a six-sided die. Here are some events:

Event A: "Rolling an even number" = {2, 4, 6}
Event B: "Rolling a number less than 3" = {1, 2}
Event C: "Rolling a 5" = {5}

Notice that events can have multiple outcomes (A and B) or just one outcome (C).

Types of Events

Simple Event: Contains only one outcome (like rolling a specific number)
Compound Event: Contains multiple outcomes (like rolling an even number)
Certain Event: Will definitely happen (like rolling a number between 1 and 6)
Impossible Event: Cannot happen (like rolling a 7 on a standard die)

Practice Question 3

In a deck of cards, the event "drawing a heart" contains how many outcomes? (Note: A standard deck has 13 hearts)

4. Calculating Basic Probability

Now let's learn how to calculate the probability of an event!

Probability Formula:
P(Event) = Number of favorable outcomes / Total number of possible outcomes

Example: Card Probability

In a standard deck of 52 cards, what's the probability of drawing a red card?

♥️

♦️

♠️

♣️

Solution:

Total cards = 52
Red cards (hearts + diamonds) = 26
P(Red) = 26/52 = 1/2 = 0.5 = 50%

Example: Multiple Outcomes

What's the probability of rolling a prime number on a six-sided die?

Solution:

Sample space: {1, 2, 3, 4, 5, 6}
Prime numbers in sample space: {2, 3, 5}
Number of favorable outcomes = 3
Total outcomes = 6
P(Prime) = 3/6 = 1/2 = 0.5 = 50%

Remember:

Probability is always between 0 and 1 (inclusive)
The sum of probabilities of all outcomes in a sample space equals 1
P(Event happens) + P(Event doesn't happen) = 1

Practice Question 4

A bag contains 4 green marbles, 3 blue marbles, and 2 yellow marbles. What is the probability of randomly picking a blue marble?

🎯 Lesson Summary

Congratulations! You've learned the fundamental concepts of probability:

✅ Probability measures the likelihood of events (0 to 1)
✅ Random experiments have uncertain but known possible outcomes
✅ Sample space contains all possible outcomes
✅ Events are collections of outcomes we're interested in
✅ Basic probability formula: Favorable outcomes ÷ Total outcomes

Next lesson: We'll explore more complex probability concepts including conditional probability and independent events!

🎲 Introduction to Probability Basics