What is Impossible Event?

S1-SA4-0324

Grade Level:

Class 2

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

An impossible event is something that can never happen. Its probability (chance of happening) is always 0. It's like trying to make something happen that is just not possible in any way.

Simple Example

Quick Example

Imagine you have a bag full of only red ladoos. If you close your eyes and pick one ladoo from the bag, what is the chance of picking a blue ladoo? It's impossible, right? So, picking a blue ladoo is an impossible event.

Worked Example

Step-by-Step

Let's say you have a standard dice with numbers 1, 2, 3, 4, 5, 6 on its faces.

---1. We want to find the probability of rolling a number 7.

---2. First, list all possible outcomes when you roll a dice: {1, 2, 3, 4, 5, 6}. There are 6 possible outcomes.

---3. Next, identify the number of favourable outcomes (how many times a 7 can appear). A standard dice does not have a 7.

---4. So, the number of favourable outcomes for rolling a 7 is 0.

---5. The formula for probability is: (Number of Favourable Outcomes) / (Total Number of Possible Outcomes).

---6. Probability of rolling a 7 = 0 / 6.

---7. 0 divided by any number is 0.

---8. So, the probability of rolling a 7 is 0. This means rolling a 7 is an impossible event.

Why It Matters

Understanding impossible events helps us make smart decisions and predict outcomes in real life. It's crucial in fields like data science for analyzing risks, in finance for understanding investment chances, and even in AI to program systems that don't try to do the impossible. Engineers use this concept to design safe bridges or reliable software.

Common Mistakes

MISTAKE: Confusing an impossible event with an unlikely event | CORRECTION: An impossible event has a probability of exactly 0 (it CANNOT happen). An unlikely event has a very small probability (close to 0, but not 0), meaning it can still happen, just rarely.

MISTAKE: Thinking that 'very difficult' means 'impossible' | CORRECTION: If there's even a tiny chance, it's not impossible. Impossible means absolutely no chance, zero probability.

MISTAKE: Assigning a negative probability to an impossible event | CORRECTION: Probability can never be less than 0. The probability of an impossible event is exactly 0, not -1 or any other negative number.

Practice Questions

Try It Yourself

QUESTION: What is the probability of a human being able to fly without any equipment? | ANSWER: 0

QUESTION: You have a box with 10 green marbles. What is the probability of picking a yellow marble from this box? | ANSWER: 0

QUESTION: A spinner has sections numbered 1 to 5. What is the probability of landing on a number greater than 5? | ANSWER: 0

MCQ

Quick Quiz

Which of these describes an impossible event?

The sun rising from the west tomorrow.

It raining on a sunny day.

Getting a 6 when rolling a dice.

Flipping a coin and getting heads.

The Correct Answer Is:

The sun always rises from the east, so it rising from the west is an impossible event. The other options are possible, even if some are less likely.

Real World Connection

In the Real World

Imagine a cricket match. Predicting a team scoring 1000 runs in a T20 match is an impossible event because the maximum balls are limited. In online banking, if a system tries to process a payment from an account with zero balance and no overdraft facility, it's an impossible transaction, and the system is designed to prevent it.

Key Vocabulary

Key Terms

PROBABILITY: The chance of something happening | EVENT: An outcome or a set of outcomes in an experiment | OUTCOME: A possible result of an experiment | CERTAIN EVENT: An event that is sure to happen (probability 1)

What's Next

What to Learn Next

Now that you understand impossible events, you can learn about 'Certain Events' which have a probability of 1. Then, you can explore how probabilities work for events that are neither impossible nor certain, which is where most real-world situations fall!