Likely, Unlikely, Certain and Impossible
Some things are sure to happen, some things can never happen, and some things might or might not happen. In mathematics, we use special words to describe the chance (or probability) of an event happening.
In Class 4, you will learn to classify events as certain, likely, unlikely, or impossible. This is the foundation of probability — an important branch of mathematics used in weather forecasts, games, and decision-making.
What is Likely, Unlikely, Certain and Impossible - Class 4 Maths (Data Handling)?
The chance of an event tells us how possible it is for that event to happen.
| Word | Meaning | Example |
|---|---|---|
| Certain | It will definitely happen | The sun will rise tomorrow |
| Likely | It will probably happen (good chance) | It will rain on a cloudy day |
| Unlikely | It probably will not happen (small chance) | It will snow in Chennai |
| Impossible | It can never happen | A dog will fly |
Between likely and unlikely, there is equally likely — when both outcomes have the same chance, like tossing a coin (heads or tails).
Solved Examples
Example 1: Example 1: Classifying everyday events
Problem: Classify each event: (a) Monday comes after Sunday. (b) A cow will talk. (c) You will roll a 6 on a dice.
Solution:
(a) Monday always follows Sunday → Certain
(b) Cows cannot talk → Impossible
(c) You might roll a 6, but it is just 1 out of 6 outcomes → Unlikely
Answer: (a) Certain, (b) Impossible, (c) Unlikely.
Example 2: Example 2: Coin toss
Problem: Aman tosses a fair coin. Is getting heads certain, likely, unlikely, or impossible?
Solution:
Step 1: A coin has 2 sides: heads and tails.
Step 2: Both outcomes are equally possible — 1 out of 2 chance.
Answer: Getting heads is equally likely (not certain, not impossible — 50% chance).
Example 3: Example 3: Coloured marbles
Problem: A bag has 8 red marbles and 2 blue marbles. Priya picks one without looking. Is picking a red marble likely or unlikely?
Solution:
Step 1: Total marbles = 10. Red = 8, Blue = 2.
Step 2: 8 out of 10 marbles are red — that is a high chance.
Answer: Picking a red marble is likely. Picking a blue marble is unlikely.
Example 4: Example 4: All same items
Problem: A box has 5 green balls and nothing else. Dev picks one ball. What is the chance of picking a green ball?
Solution:
Step 1: Every ball in the box is green.
Step 2: No matter which ball Dev picks, it will be green.
Answer: Picking a green ball is certain. Picking any other colour is impossible.
Example 5: Example 5: Dice roll
Problem: Meera rolls a regular dice. Is it likely to get a number less than 5?
Solution:
Step 1: Numbers on a dice: 1, 2, 3, 4, 5, 6.
Step 2: Numbers less than 5: 1, 2, 3, 4 → that is 4 out of 6 outcomes.
Step 3: 4 out of 6 is more than half — good chance.
Answer: Getting a number less than 5 is likely.
Example 6: Example 6: Spinner
Problem: A spinner is divided into 4 equal parts — 3 parts are yellow and 1 part is blue. What is the chance of landing on yellow?
Solution:
Step 1: Yellow sections = 3, Blue sections = 1, Total = 4.
Step 2: 3 out of 4 sections are yellow — that is a high chance.
Answer: Landing on yellow is likely. Landing on blue is unlikely.
Example 7: Example 7: Impossible vs unlikely
Problem: (a) A fish will climb a tree. (b) It will snow in Delhi in July. Are these impossible or unlikely?
Solution:
(a) Fish cannot climb trees. This can never happen → Impossible.
(b) Snow in Delhi in July is extremely rare, but not absolutely impossible in unusual weather → Unlikely.
Answer: (a) Impossible, (b) Unlikely. An impossible event can never happen under any condition, while an unlikely event has a very small chance.
Example 8: Example 8: Number cards
Problem: Cards numbered 1 to 10 are placed in a box. Arjun draws one card. Is drawing an even number likely, unlikely, or equally likely?
Solution:
Step 1: Even numbers: 2, 4, 6, 8, 10 → 5 cards
Step 2: Odd numbers: 1, 3, 5, 7, 9 → 5 cards
Step 3: 5 out of 10 = half the cards are even.
Answer: Drawing an even number is equally likely (same chance as drawing an odd number).
Example 9: Example 9: Weather prediction
Problem: The sky is dark and cloudy. Is it likely or unlikely to rain?
Solution:
Step 1: Dark clouds usually bring rain.
Step 2: While not certain (clouds sometimes pass without rain), the chance is high.
Answer: Rain is likely when the sky is dark and cloudy.
Example 10: Example 10: Ordering by chance
Problem: Put these events in order from impossible to certain: (A) Drawing a red card from a bag of 10 red cards, (B) Rolling a 7 on a regular dice, (C) It will rain this year in Mumbai, (D) Picking a blue marble from a bag of 1 blue and 9 red marbles.
Solution:
(B) Rolling a 7 → Impossible (dice has only 1–6)
(D) Blue from 1 blue + 9 red → Unlikely (1 out of 10)
(C) Rain in Mumbai this year → Likely (Mumbai gets monsoon rain every year)
(A) Red from all red → Certain
Answer: Order: B (Impossible) → D (Unlikely) → C (Likely) → A (Certain)
Key Points to Remember
- Certain: The event will definitely happen (100% chance).
- Likely: The event has a good chance of happening (more than half).
- Equally likely: Both outcomes have the same chance (exactly half).
- Unlikely: The event has a small chance (less than half).
- Impossible: The event can never happen (0% chance).
- The order from lowest to highest chance: Impossible → Unlikely → Equally likely → Likely → Certain.
- Count favourable outcomes and total outcomes to decide the category.
Practice Problems
- Classify: (a) The sun sets in the west. (b) You will meet a dinosaur today. (c) You roll an even number on a dice.
- A bag has 7 yellow and 3 green balls. Is picking yellow likely or unlikely?
- A spinner has 6 equal parts: 5 red and 1 blue. What is the chance of landing on blue — likely, unlikely, or impossible?
- Is it certain, likely, unlikely, or impossible that February has 30 days?
- Cards numbered 1 to 20 are in a bag. Is drawing a number greater than 15 likely or unlikely?
- Put in order from impossible to certain: (A) A cat will bark. (B) You will eat food today. (C) It might rain tomorrow.
Frequently Asked Questions
Q1. What does 'likely' mean in maths?
Likely means the event has a good chance of happening — more favourable outcomes than unfavourable ones. It is not guaranteed but is expected to happen more often than not.
Q2. What is the difference between unlikely and impossible?
Unlikely means there is a small chance — it could happen but probably will not. Impossible means it can never happen under any circumstances. Getting a 6 on a dice is unlikely; getting a 7 is impossible.
Q3. What does 'equally likely' mean?
Equally likely means both outcomes have the same chance. When you toss a fair coin, heads and tails are equally likely — each has a 1 out of 2 chance.
Q4. How do you decide if an event is likely or unlikely?
Count the favourable outcomes and compare to the total outcomes. If favourable is more than half the total, it is likely. If less than half, it is unlikely. If exactly half, it is equally likely.
Q5. Is getting a 6 on a dice likely or unlikely?
Unlikely. There is only 1 favourable outcome (6) out of 6 possible outcomes. Since 1 out of 6 is less than half, rolling a 6 is unlikely.
Q6. Can a likely event not happen?
Yes. Likely means it has a good chance, not that it is guaranteed. For example, if a bag has 9 red and 1 blue marble, picking red is likely, but you could still pick the blue one.
Q7. What are some examples of certain events?
The sun rising in the east, Tuesday coming after Monday, water freezing at 0°C — these are all certain events. They will always happen.
Q8. Is this topic related to probability?
Yes. Likely, unlikely, certain, and impossible are introductory probability concepts. In higher classes, you will assign numbers (0 to 1) to represent the exact chance of events.
