What is an Impossible Event's Probability?

S7-SA3-0416

Grade Level:

Class 12

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

Definition

What is it?

The probability of an impossible event is 0. An impossible event is something that can never happen, no matter what. It has no chance of occurring.

Simple Example

Quick Example

Imagine a cricket match where Team A needs 10 runs to win, and Team B needs 50 runs. If the match is over and Team A wins, it's impossible for Team B to have won. So, the probability of Team B winning after Team A has already won is 0.

Worked Example

Step-by-Step

QUESTION: What is the probability of picking a blue ball from a bag that only contains red balls? --- STEP 1: Identify the event. The event is 'picking a blue ball'. --- STEP 2: Look at the sample space. The bag only has red balls. There are no blue balls at all. --- STEP 3: Determine the number of favorable outcomes. Since there are no blue balls, the number of favorable outcomes (picking a blue ball) is 0. --- STEP 4: Determine the total number of possible outcomes. Let's say there are 10 red balls. So, the total number of balls is 10. --- STEP 5: Calculate the probability. Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 0 / 10. --- STEP 6: Simplify the probability. 0 / 10 = 0. --- ANSWER: The probability of picking a blue ball is 0.

Why It Matters

Understanding impossible events helps in making smart decisions in AI/ML, like knowing a self-driving car cannot suddenly fly. In medicine, it helps doctors understand that a patient cannot recover from a certain stage of a disease if it's medically impossible. Engineers use this to design safe systems, knowing certain failures have zero probability.

Common Mistakes

MISTAKE: Confusing an impossible event with an unlikely event. | CORRECTION: An impossible event CANNOT happen (probability 0). An unlikely event CAN happen but rarely (probability close to 0, but not 0). For example, winning a lottery is unlikely, not impossible.

MISTAKE: Saying an impossible event has 'very low' probability. | CORRECTION: The probability of an impossible event is exactly 0, not 'very low'. There's a big difference between something that has a tiny chance and something that has no chance at all.

MISTAKE: Assuming an event is impossible just because it hasn't happened yet. | CORRECTION: An event is impossible only if it fundamentally cannot occur based on the rules or conditions. For example, it's impossible to roll a 7 on a standard six-sided dice, but it's not impossible to flip a coin 100 times and get all heads, just extremely unlikely.

Practice Questions

Try It Yourself

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

QUESTION: A spinner has sections numbered 1, 2, 3, and 4. What is the probability of landing on the number 5 in one spin? | ANSWER: 0

QUESTION: In a standard deck of 52 playing cards, what is the probability of drawing a card that is both a King and a 7 at the same time? | ANSWER: 0

MCQ

Quick Quiz

Which of the following describes an impossible event?

An event that is very difficult to happen.

An event that has a 50% chance of happening.

An event that has no chance of happening.

An event that is guaranteed to happen.

The Correct Answer Is:

An impossible event is defined as an event that cannot occur under any circumstances, meaning it has zero probability. Options A and B describe possible events, while option D describes a sure event.

Real World Connection

In the Real World

When you use a navigation app like Google Maps or Ola, it calculates the estimated time of arrival. It's an impossible event for the app to predict you'll reach your destination in 5 minutes if it's 50 km away, assuming normal traffic and no special transport. Such calculations rely on understanding what's realistically possible and what's impossible.

Key Vocabulary

Key Terms

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

What's Next

What to Learn Next

Next, you should learn about 'Sure Events' and their probability. It's the complete opposite of impossible events and will help you understand the full range of probability from 0 to 1.