What is the Probability of an Impossible Event?

S7-SA3-0313

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 a measure of how likely it is for an event that can never happen to occur. Since such an event has no chance of happening, its probability is always 0. It represents absolute certainty that the event will not take place.

Simple Example

Quick Example

Imagine you have a standard six-sided dice with faces numbered 1 to 6. What is the probability of rolling a 7? Since there is no face with the number 7 on the dice, it's impossible to roll a 7. So, the probability of rolling a 7 is 0.

Worked Example

Step-by-Step

Let's find the probability of picking a blue marble from a bag that only contains red marbles.
---Step 1: Identify the total number of possible outcomes. Suppose the bag has 5 red marbles. So, total outcomes = 5.
---Step 2: Identify the number of favorable outcomes for picking a blue marble. Since there are no blue marbles in the bag, the number of favorable outcomes is 0.
---Step 3: Apply the probability formula: Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes).
---Step 4: Substitute the values: Probability = 0 / 5.
---Step 5: Calculate the result: Probability = 0.
---Answer: The probability of picking a blue marble is 0.

Why It Matters

Understanding impossible events is crucial in fields like AI/ML to set boundaries for predictions, and in engineering to design systems that avoid impossible failures. For instance, in FinTech, it helps identify scenarios with zero chance of occurring, guiding safer investment strategies. Engineers use this to ensure that a bridge, for example, has a 0 probability of collapsing under normal load.

Common Mistakes

MISTAKE: Thinking an impossible event has a very small, but not zero, probability (e.g., 0.000001). | CORRECTION: An impossible event has a probability of exactly 0, meaning it can absolutely never happen.

MISTAKE: Confusing an impossible event with a very unlikely event. | CORRECTION: An unlikely event might have a very small probability (e.g., winning a lottery), but an impossible event has zero probability.

MISTAKE: Assuming that if an event didn't happen, it was impossible. | CORRECTION: An event might not happen (e.g., it didn't rain today), but it wasn't impossible unless there was absolutely no way for it to occur.

Practice Questions

Try It Yourself

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

QUESTION: A spinner has sections numbered 1, 2, 3, and 4. What is the probability of the spinner landing on the number 5? | 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 Queen at the same time? | ANSWER: 0

MCQ

Quick Quiz

Which of the following describes the probability of an impossible event?

A very small number close to 0

Exactly 0

Cannot be determined

The Correct Answer Is:

An impossible event is an event that can never happen, so its probability is always exactly 0. Options A suggests it might happen, while C means it's certain to happen.

Real World Connection

In the Real World

In cricket analytics, if a team needs 100 runs to win on the last ball of the match, the probability of them winning is 0, as it's an impossible score to achieve from a single ball. Similarly, when you use a UPI app to send money, the probability of the money disappearing without a trace is practically 0 due to robust system design and security measures.

Key Vocabulary

Key Terms

Probability: The chance of an event happening, expressed as a number between 0 and 1 | Event: A specific outcome or a set of outcomes in an experiment | Outcome: A possible result of an experiment or trial | Certain Event: An event that is sure to happen, with a probability of 1 | Sample Space: The set of all possible outcomes of an experiment

What's Next

What to Learn Next

Now that you understand impossible events, next you should explore 'What is the Probability of a Certain Event?' This will complete your understanding of the two extreme ends of the probability scale, from impossible to guaranteed.