What is Impossible (Probability)?

S1-SA4-0554

Grade Level:

Class 5

Maths, Data Science, AI, Statistics, Logic

Definition

What is it?

In probability, 'impossible' means an event that can never happen. The chance of an impossible event occurring is zero. It's like trying to get something that simply doesn't exist or cannot physically occur.

Simple Example

Quick Example

Imagine you have a box full of only red ladoos. If you close your eyes and pick a ladoo from the box, what is the chance of picking a green ladoo? It's impossible because there are no green ladoos in the box.

Worked Example

Step-by-Step

Let's say your school principal announces that tomorrow, all students will get a free bicycle. This is a very exciting event!

STEP 1: Identify the event: Getting a free bicycle tomorrow.
---STEP 2: Look at the current situation: Is there any plan or budget for giving free bicycles to all students tomorrow? No, it was just a fun announcement.
---STEP 3: Consider the practical possibility: Can the school arrange hundreds of bicycles for all students in just one day? It's highly unlikely and not planned.
---STEP 4: Determine the probability: Since there's no actual plan and it's not practical to arrange, the event of 'all students getting a free bicycle tomorrow' is impossible. The probability is 0.
---ANSWER: The event is impossible.

Why It Matters

Understanding impossible events helps us make smart predictions and decisions in everyday life. It's a basic building block for advanced fields like Data Science and AI, where people analyze huge amounts of information to predict outcomes. Engineers, scientists, and even cricket match analysts use these concepts to understand what can and cannot happen.

Common Mistakes

MISTAKE: Confusing 'very unlikely' with 'impossible'. For example, thinking it's impossible for India to win a cricket match if they need 100 runs in 1 over. | CORRECTION: While very unlikely, it's not impossible (e.g., if many no-balls or wides are bowled, or multiple sixes). Impossible means literally 0% chance, like picking a yellow ball from a bag with only blue balls.

MISTAKE: Believing an event is impossible just because it hasn't happened yet. For example, thinking it's impossible to score 100% in a math test because you haven't done it before. | CORRECTION: An event is only impossible if there is no way for it to occur, not just because it's difficult or rare. Scoring 100% is difficult, but definitely possible.

MISTAKE: Not checking all conditions before declaring an event impossible. For example, saying it's impossible to get a 7 when rolling a standard 6-sided dice. | CORRECTION: This is correct for a standard 6-sided dice. However, if it were a custom dice with faces 1 to 8, then getting a 7 would be possible. Always understand the full context of the situation.

Practice Questions

Try It Yourself

QUESTION: What is the probability of the sun rising from the West tomorrow? | ANSWER: Impossible (Probability is 0)

QUESTION: A bag contains 5 red pens and 3 blue pens. What is the probability of picking a green pen from the bag? | ANSWER: Impossible (Probability is 0)

QUESTION: You are playing Ludo with a standard dice (numbers 1 to 6). Your friend says it's impossible to roll an even number. Is your friend correct? Explain why. | ANSWER: No, your friend is incorrect. It is possible to roll an even number (2, 4, or 6) on a standard dice. So, it is not an impossible event.

MCQ

Quick Quiz

Which of the following events is impossible?

Rolling a '6' on a standard six-sided dice

Picking a black card from a deck of only red cards

Getting heads when flipping a coin

It raining on a summer day

The Correct Answer Is:

Picking a black card from a deck of only red cards is impossible because there are no black cards present. All other options describe events that are possible, even if they don't happen every time.

Real World Connection

In the Real World

When weather forecasters predict 'zero chance of rain,' they are talking about an impossible event for that specific time. Similarly, in cricket, if a team needs 100 runs from 1 ball, it's considered an impossible win unless there are extraordinary, rule-breaking circumstances. Even in online shopping, if a product is 'out of stock' everywhere, it's practically impossible to buy it right then.

Key Vocabulary

Key Terms

PROBABILITY: The chance of an event happening | EVENT: Something that can happen or occur | CERTAIN EVENT: An event that will definitely happen (probability 1) | UNLIKELY: An event that has a very small chance of happening, but is not impossible

What's Next

What to Learn Next

Great job understanding impossible events! Next, you can learn about 'Certain Events' in probability. This will help you understand the full range of possibilities, from things that can never happen to things that will definitely happen.