Probability Introduction (Grade 5)
Probability is the study of how likely an event is to happen. Some events are certain (the sun will rise tomorrow), some are impossible (you will fly without wings), and most are somewhere in between.
In Class 5, probability is introduced through everyday language: certain, likely, equally likely, unlikely, impossible. You will also learn to express probability as a simple fraction: the number of favourable outcomes divided by the total number of outcomes.
Probability helps us make predictions and decisions. Weather forecasts, games, sports strategies, and even choosing what to wear all involve thinking about probability.
What is Probability Introduction - Class 5 Maths (Data Handling)?
Probability is a measure of how likely an event is to occur.
- Certain event: Will definitely happen. Probability = 1.
- Impossible event: Cannot happen. Probability = 0.
- Likely event: Has a good chance of happening.
- Unlikely event: Has a small chance of happening.
- Equally likely: All outcomes have the same chance (like tossing a fair coin).
Probability = Number of favourable outcomes ÷ Total number of outcomes
Types and Properties
Probability scale:
0 ——— unlikely ——— equally likely ——— likely ——— 1
impossible certain
Types of events:
- Random experiment: An activity where the outcome is not known beforehand (tossing a coin, rolling a dice).
- Outcome: A possible result of an experiment.
- Favourable outcome: The outcome we are looking for.
- Sample space: The set of all possible outcomes.
Solved Examples
Example 1: Example 1: Certain, Likely, or Impossible
Problem: Classify each event: (a) The sun rises in the east. (b) A cat speaks English. (c) It rains in July in Mumbai.
Solution:
(a) Certain — this always happens.
(b) Impossible — this cannot happen.
(c) Likely — Mumbai gets heavy rain in July (monsoon), so this has a high chance.
Example 2: Example 2: Tossing a Coin
Problem: A fair coin is tossed. What is the probability of getting Heads?
Solution:
Total outcomes = 2 (Heads, Tails)
Favourable outcomes (Heads) = 1
Probability = 1/2
Answer: The probability of Heads is 1/2 (or 0.5).
Example 3: Example 3: Rolling a Dice
Problem: A fair dice is rolled. What is the probability of getting a 4?
Solution:
Total outcomes = 6 (1, 2, 3, 4, 5, 6)
Favourable outcomes (getting 4) = 1
Probability = 1/6
Answer: The probability of getting 4 is 1/6.
Example 4: Example 4: Even Number on a Dice
Problem: What is the probability of rolling an even number on a dice?
Solution:
Even numbers on a dice: 2, 4, 6 = 3 favourable outcomes.
Total outcomes = 6.
Probability = 3/6 = 1/2.
Answer: The probability is 1/2.
Example 5: Example 5: Picking a Ball from a Bag
Problem: A bag has 3 red balls, 2 blue balls, and 5 green balls. Priya picks one ball without looking. What is the probability that it is red?
Solution:
Total balls = 3 + 2 + 5 = 10
Red balls (favourable) = 3
Probability = 3/10
Answer: The probability of picking a red ball is 3/10.
Example 6: Example 6: Spinner
Problem: A spinner has 8 equal sections: 3 yellow, 2 blue, 1 red, 2 green. What is the probability of landing on blue?
Solution:
Total sections = 8. Blue sections = 2.
Probability = 2/8 = 1/4.
Answer: The probability of landing on blue is 1/4.
Example 7: Example 7: Impossible Event
Problem: A bag has only red and blue balls. What is the probability of picking a green ball?
Solution:
There are no green balls. Favourable outcomes = 0.
Probability = 0/total = 0.
Answer: The probability is 0 (impossible).
Example 8: Example 8: Certain Event
Problem: A box has 5 mangoes and nothing else. Aman picks a fruit from the box. What is the probability that it is a mango?
Solution:
All fruits are mangoes. Favourable = 5, Total = 5.
Probability = 5/5 = 1.
Answer: The probability is 1 (certain).
Example 9: Example 9: Comparing Probabilities
Problem: In a dice roll, is it more likely to get a number greater than 4 or a number less than 3?
Solution:
Greater than 4: {5, 6} = 2 outcomes. Probability = 2/6 = 1/3.
Less than 3: {1, 2} = 2 outcomes. Probability = 2/6 = 1/3.
Answer: Both events are equally likely (probability 1/3 each).
Example 10: Example 10: Picking a Card
Problem: Kavi has cards numbered 1 to 10. He picks one card randomly. What is the probability of picking a multiple of 3?
Solution:
Multiples of 3 from 1 to 10: 3, 6, 9 = 3 favourable outcomes.
Total outcomes = 10.
Probability = 3/10.
Answer: The probability is 3/10.
Real-World Applications
Where do we use probability?
- Weather: “70% chance of rain” is a probability statement.
- Games: Board games, card games, and dice games all involve probability.
- Sports: A cricket team’s chance of winning depends on team form, conditions, etc.
- Medicine: Doctors use probability to predict treatment success rates.
- Daily decisions: Choosing to carry an umbrella, picking a route to school.
Key Points to Remember
- Probability measures how likely an event is to happen.
- Probability = favourable outcomes ÷ total outcomes.
- Probability ranges from 0 (impossible) to 1 (certain).
- All equally likely outcomes have the same probability.
- Tossing a fair coin: P(Heads) = P(Tails) = 1/2.
- Rolling a fair dice: P(any single number) = 1/6.
- More favourable outcomes = higher probability.
- The sum of probabilities of all possible outcomes = 1.
Practice Problems
- A fair dice is rolled. What is the probability of getting a number less than 5?
- A bag has 4 red, 3 blue, and 3 white balls. What is the probability of picking a blue ball?
- Classify: (a) A fish living underwater. (b) Rolling a 7 on a standard dice. (c) Getting rain in December in Chennai.
- A spinner has 6 equal sections numbered 1 to 6. What is the probability of landing on an odd number?
- Meera picks a card from cards numbered 1 to 20. What is the probability of picking an even number?
- A bag has 8 green balls only. What is the probability of picking a green ball?
- A coin is tossed twice. List all possible outcomes (sample space).
- Arjun says the probability of an event is 5/3. Is this possible? Why or why not?
Frequently Asked Questions
Q1. What is probability?
Probability is a measure of how likely an event is to happen. It is expressed as a number from 0 (impossible) to 1 (certain).
Q2. How do you calculate probability?
Probability = number of favourable outcomes divided by total number of possible outcomes. All outcomes must be equally likely.
Q3. What is a sample space?
The sample space is the set of all possible outcomes. For a dice, it is {1, 2, 3, 4, 5, 6}. For a coin, it is {Heads, Tails}.
Q4. What does probability 0 mean?
Probability 0 means the event is impossible. It cannot happen. For example, rolling a 7 on a standard dice has probability 0.
Q5. What does probability 1 mean?
Probability 1 means the event is certain. It will definitely happen. For example, picking a red ball from a bag that contains only red balls.
Q6. Can probability be greater than 1?
No. Probability always lies between 0 and 1 (inclusive). A value greater than 1 or less than 0 is not valid.
Q7. What are equally likely outcomes?
Outcomes that have the same chance of occurring. A fair coin has equally likely outcomes (Heads and Tails each have probability 1/2).
Q8. What is the difference between likely and certain?
A likely event has a high probability but can still not happen. A certain event has probability 1 and will definitely happen.
Q9. Is probability taught in NCERT Class 5?
Yes. Introduction to probability using everyday language (certain, likely, unlikely, impossible) and simple fractions is part of the Data Handling chapter in NCERT/CBSE Class 5 Maths.
