Probability Basics
In everyday life, we often talk about chances. We say things like:
- It may rain today
- This team has a high chance of winning
- There is a low chance of failure
Probability is the branch of statistics that measures how likely an event is to occur.
What Is Probability?
Probability is a numerical measure that describes the likelihood of an event.
The value of probability always lies between:
- 0 → Event will not happen
- 1 → Event will definitely happen
A probability closer to 1 means the event is more likely.
Basic Probability Formula
The basic formula for probability is:
Probability = Number of favorable outcomes ÷ Total number of possible outcomes
This formula applies when all outcomes are equally likely.
Numerical Example
A bag contains 5 red balls and 5 blue balls. One ball is drawn at random.
Total possible outcomes = 10
Favorable outcomes (red ball) = 5
Probability of drawing a red ball:
5 ÷ 10 = 0.5
So, there is a 50% chance of drawing a red ball.
Real-World Example
If a weather forecast says there is a 70% chance of rain, it means rain is more likely to happen than not.
However, it does not guarantee that it will rain.
Types of Events
In probability, events are commonly classified into different types.
Impossible Event
An event that cannot happen.
Example: Rolling a 7 on a standard six-sided die.
Certain Event
An event that will always happen.
Example: Getting a number between 1 and 6 when rolling a die.
Possible Event
An event that may or may not happen.
Example: Tossing a coin and getting heads.
Probability of Common Experiments
| Experiment | Event | Probability |
|---|---|---|
| Coin Toss | Getting Heads | 1/2 |
| Die Roll | Getting an Even Number | 3/6 = 1/2 |
| Card Draw | Getting a Heart | 13/52 = 1/4 |
Key Properties of Probability
- Probability is always between 0 and 1
- The sum of probabilities of all possible outcomes is 1
- Higher probability means higher chance of occurrence
Quick Check
If the probability of an event is 0, what does it mean?
Practice Quiz
Question 1:
What is the probability of getting tails when tossing a fair coin?
Question 2:
What is the probability of rolling a number greater than 4 on a die?
Question 3:
Which probability value represents a certain event?
Mini Practice
A box contains 3 green balls and 7 yellow balls. One ball is picked randomly.
- What is the probability of picking a green ball?
- Is picking a yellow ball more likely?
What’s Next
In the next lesson, we will study Basic Probability Rules, which explain how probabilities behave when events are combined.