What is an Impossible Event?

S7-SA3-0008

Grade Level:

Class 12

AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics

Definition

What is it?

An impossible event is an event that can never happen. Its probability is always 0, meaning there is no chance of it occurring under any circumstances.

Simple Example

Quick Example

Imagine you are playing Ludo with a standard dice. An impossible event would be rolling an 8, because a standard Ludo dice only has faces numbered 1 to 6. It's simply not possible.

Worked Example

Step-by-Step

Let's say a school bag contains 5 red pens and 3 blue pens. We want to find the probability of picking a green pen from this bag.
---Total number of pens in the bag = Number of red pens + Number of blue pens = 5 + 3 = 8 pens.
---Number of green pens in the bag = 0 (since there are no green pens).
---The formula for probability is: P(Event) = (Number of favorable outcomes) / (Total number of possible outcomes).
---For picking a green pen, the number of favorable outcomes is 0.
---So, P(picking a green pen) = 0 / 8.
---P(picking a green pen) = 0.
---Therefore, picking a green pen from this bag is an impossible event.

Why It Matters

Understanding impossible events helps in making smart decisions, whether it's in AI/ML for predicting outcomes, or in FinTech for assessing investment risks. Engineers use this concept to design safe systems, like making sure a bridge won't collapse under normal conditions. It's key to building reliable technology and making informed choices in many careers.

Common Mistakes

MISTAKE: Thinking an event with a very low probability (like 0.0001) is impossible. | CORRECTION: An impossible event has a probability of exactly 0. A very low probability means it's highly unlikely, but still has a tiny chance.

MISTAKE: Confusing an impossible event with a certain event. | CORRECTION: An impossible event has a probability of 0 (it cannot happen), while a certain event has a probability of 1 (it will definitely happen).

MISTAKE: Assuming an event is impossible just because it hasn't happened yet. | CORRECTION: An event is impossible only if its occurrence is logically or physically impossible, not just because it's rare or hasn't been observed.

Practice Questions

Try It Yourself

QUESTION: What is the probability of a standard coin landing on its side (neither heads nor tails) when flipped? | ANSWER: 0

QUESTION: A box contains cards numbered 1 to 10. What is the probability of drawing a card with a number greater than 10? | ANSWER: 0

QUESTION: In a lottery where tickets are numbered from 1 to 100, what is the probability of drawing a ticket with the number 0? Explain your reasoning. | ANSWER: 0. Reasoning: The lottery tickets are numbered from 1 to 100, so a ticket with the number 0 does not exist in the set of possible outcomes.

MCQ

Quick Quiz

Which of the following describes an impossible event?

An event that has a very low chance of happening.

An event that has a probability of 1.

An event that cannot happen under any circumstances.

An event that is difficult to predict.

The Correct Answer Is:

An impossible event is defined as an event that cannot happen, meaning its probability is exactly 0. Option C correctly captures this definition. Options A, B, and D describe unlikely, certain, or unpredictable events, respectively, not impossible ones.

Real World Connection

In the Real World

Imagine you are using a weather app on your phone, like AccuWeather or IMD. The app predicting a snowstorm in Chennai in July would be an impossible event, as Chennai's climate does not support snow. Data scientists working on such apps use probability to filter out such impossible predictions, ensuring the information you receive is realistic and useful.

Key Vocabulary

Key Terms

PROBABILITY: The chance of an event happening, expressed as a number between 0 and 1. | OUTCOME: A possible result of an experiment or event. | SAMPLE SPACE: The set of all possible outcomes of an experiment. | CERTAIN EVENT: An event that is sure to happen, with a probability of 1.

What's Next

What to Learn Next

Now that you understand impossible events, you should explore 'Certain Events' and 'Types of Events in Probability'. These concepts will help you build a complete picture of how probability works, from events that definitely won't happen to those that definitely will.