Chance and Probability Introduction
Will it rain today? Will your team win the match? Will you get a 6 when you roll a dice? These questions involve chance — something that may or may not happen.
In mathematics, we use probability to measure how likely an event is to happen. Probability gives a number between 0 and 1 to describe the chance of an event.
In Class 7 NCERT Maths, you will learn the basic ideas of chance and probability using simple experiments like tossing a coin, rolling a dice, and picking cards.
What is Chance and Probability Introduction - Grade 7 Maths (Data Handling)?
Definition: Probability is a measure of how likely an event is to occur. It is a number between 0 and 1.
- If an event is impossible (can never happen), its probability is 0.
- If an event is certain (will definitely happen), its probability is 1.
- If an event may or may not happen, its probability is between 0 and 1.
Key terms:
- Experiment: An action that produces a result (e.g., tossing a coin).
- Outcome: A possible result of an experiment (e.g., getting heads).
- Event: A collection of one or more outcomes (e.g., getting an even number on a dice).
Chance and Probability Introduction Formula
Formula for probability:
Probability of an event = Number of favourable outcomes / Total number of outcomes
Where:
- Favourable outcomes = the outcomes where the event happens
- Total outcomes = all possible outcomes of the experiment
Important:
- Probability is always between 0 and 1 (inclusive).
- Probability can also be written as a fraction, decimal, or percentage.
Types and Properties
Types of events:
- Certain event: An event that will always happen. Probability = 1. Example: Getting a number less than 7 when rolling a dice.
- Impossible event: An event that can never happen. Probability = 0. Example: Getting a 7 when rolling a standard dice.
- Likely event: An event that has a good chance of happening. Example: Getting a number less than 5 on a dice (4 out of 6 chance).
- Unlikely event: An event that has a small chance. Example: Getting a 6 on a dice (1 out of 6).
- Equally likely events: Events that have the same chance of happening. Example: Getting heads or tails on a fair coin.
Solved Examples
Example 1: Tossing a Coin
Problem: A fair coin is tossed once. What is the probability of getting heads?
Solution:
Total outcomes: Heads, Tails = 2 outcomes
Favourable outcomes (heads): 1
Probability = 1/2
Answer: The probability of getting heads is 1/2 (or 0.5 or 50%).
Example 2: Rolling a Dice — Getting a 4
Problem: A fair dice is rolled. What is the probability of getting a 4?
Solution:
Total outcomes: 1, 2, 3, 4, 5, 6 = 6 outcomes
Favourable outcomes (getting 4): 1
Probability = 1/6
Answer: The probability of getting a 4 is 1/6.
Example 3: Rolling a Dice — Getting an Even Number
Problem: What is the probability of getting an even number when rolling a dice?
Solution:
Total outcomes: 1, 2, 3, 4, 5, 6 = 6
Favourable outcomes (even numbers): 2, 4, 6 = 3
Probability = 3/6 = 1/2
Answer: The probability is 1/2.
Example 4: Impossible Event
Problem: What is the probability of getting a number greater than 6 when rolling a standard dice?
Solution:
A standard dice has numbers 1 to 6. No outcome is greater than 6.
Favourable outcomes = 0
Probability = 0/6 = 0
Answer: The probability is 0 (impossible event).
Example 5: Certain Event
Problem: What is the probability of getting a number less than 7 when rolling a dice?
Solution:
All outcomes (1, 2, 3, 4, 5, 6) are less than 7.
Favourable outcomes = 6, Total outcomes = 6
Probability = 6/6 = 1
Answer: The probability is 1 (certain event).
Example 6: Drawing a Ball from a Bag
Problem: A bag contains 3 red balls, 2 blue balls, and 5 green balls. A ball is drawn at random. Find the probability of drawing a blue ball.
Solution:
Total balls: 3 + 2 + 5 = 10
Favourable (blue): 2
Probability = 2/10 = 1/5
Answer: The probability of drawing a blue ball is 1/5.
Example 7: Spinning a Spinner
Problem: A spinner has 8 equal sections numbered 1 to 8. What is the probability of landing on a number greater than 5?
Solution:
Total outcomes: 8
Favourable outcomes (6, 7, 8): 3
Probability = 3/8
Answer: The probability is 3/8.
Example 8: Picking a Card
Problem: From cards numbered 1 to 10, one card is picked at random. What is the probability of picking an odd number?
Solution:
Total outcomes: 10
Odd numbers: 1, 3, 5, 7, 9 = 5
Probability = 5/10 = 1/2
Answer: The probability is 1/2.
Example 9: Probability as a Percentage
Problem: There is a 3 out of 4 chance of rain tomorrow. Express this as a percentage.
Solution:
Probability = 3/4 = 0.75 = 75%
Answer: There is a 75% chance of rain.
Example 10: Word Problem on Chance
Problem: A box has 4 chocolates and 6 toffees. If you pick one sweet without looking, what is the probability of getting a chocolate?
Solution:
Total sweets: 4 + 6 = 10
Favourable (chocolate): 4
Probability = 4/10 = 2/5
Answer: The probability of getting a chocolate is 2/5.
Real-World Applications
Real-life uses of probability:
- Weather forecasting: "There is a 70% chance of rain" is a probability statement.
- Games: Card games, board games, and lotteries all involve probability.
- Insurance: Companies use probability to calculate the chance of events (accidents, illness) to decide premiums.
- Medicine: Doctors talk about the probability of treatment success.
- Sports: "Team A has a 60% chance of winning" is based on probability analysis.
- Decision making: Businesses use probability to assess risks before making decisions.
Key Points to Remember
- Probability measures how likely an event is to happen.
- Probability = Favourable outcomes / Total outcomes.
- Probability is always between 0 and 1 (inclusive).
- Probability 0 = impossible event. Probability 1 = certain event.
- A fair coin has equal probability for heads and tails (1/2 each).
- A fair dice has equal probability for each face (1/6 each).
- Probability can be expressed as a fraction, decimal, or percentage.
- The sum of probabilities of all outcomes of an experiment equals 1.
Practice Problems
- A dice is rolled. What is the probability of getting a number less than 3?
- A bag has 5 red, 3 blue, and 2 yellow marbles. What is the probability of picking a red marble?
- Two coins are tossed together. List all possible outcomes. What is the probability of getting two heads?
- Cards numbered 1 to 20 are in a box. What is the probability of picking a multiple of 5?
- Is the probability of an event ever greater than 1? Explain.
- A spinner has 5 equal sections coloured red, blue, green, yellow, and white. What is the probability of landing on green?
Frequently Asked Questions
Q1. What is probability in simple words?
Probability tells you how likely something is to happen. It is a number between 0 and 1. If probability is 0, the event is impossible. If probability is 1, the event is certain. A probability of 1/2 means the event is equally likely to happen or not.
Q2. What is the probability of getting heads when tossing a coin?
A fair coin has two outcomes: heads and tails. The probability of getting heads = 1/2 = 0.5 = 50%.
Q3. What is a random experiment?
A random experiment is an action where you cannot predict the exact outcome in advance, but you know all the possible outcomes. For example, rolling a dice is a random experiment because you know the outcomes are 1 to 6 but cannot predict which one will come.
Q4. Can probability be negative?
No. Probability is always between 0 and 1. It can never be negative or greater than 1.
Q5. What does equally likely mean?
Equally likely means each outcome has the same chance of occurring. For example, on a fair dice, each number (1, 2, 3, 4, 5, 6) is equally likely with probability 1/6.
Q6. What is the difference between chance and probability?
In everyday language, 'chance' and 'probability' mean the same thing — how likely something is to happen. In mathematics, probability gives a precise number (between 0 and 1) to measure that chance.
Q7. What is the sum of probabilities of all outcomes?
The sum of the probabilities of all possible outcomes of an experiment is always 1. For example, for a coin: P(heads) + P(tails) = 1/2 + 1/2 = 1.
