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What is a Sure Event?
Grade Level:
Class 12
AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics
Definition
What is it?
A Sure Event, also known as a Certain Event, is an event that is guaranteed to happen in any given experiment. Its probability is always 1, meaning it will occur 100% of the time.
Simple Example
Quick Example
Imagine you have a bag full of only red marbles. If you reach into the bag and pick out a marble, it is a sure event that you will pick a red marble. There's no other colour, so it's certain!
Worked Example
Step-by-Step
Let's say you have a standard six-sided dice, with faces numbered 1, 2, 3, 4, 5, 6. We want to find the probability of rolling a number less than 7.
Step 1: Identify all possible outcomes when rolling a dice. The sample space S = {1, 2, 3, 4, 5, 6}. So, the total number of outcomes is 6.
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Step 2: Identify the outcomes that satisfy the event 'rolling a number less than 7'. The numbers less than 7 are {1, 2, 3, 4, 5, 6}. So, the number of favourable outcomes is 6.
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Step 3: Calculate the probability using the formula: Probability = (Number of favourable outcomes) / (Total number of outcomes).
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Step 4: Probability = 6 / 6 = 1.
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Answer: The probability of rolling a number less than 7 is 1, making it a Sure Event.
Why It Matters
Understanding sure events is fundamental in fields like AI/ML, where predicting certain outcomes is key to building reliable systems. Engineers use this concept to design systems with guaranteed safety features, while economists use it to model certain market behaviors. It helps professionals make reliable predictions and build robust solutions.
Common Mistakes
MISTAKE: Confusing a sure event with an event that has a high probability (e.g., 0.99). | CORRECTION: A sure event MUST have a probability of exactly 1. Anything less than 1, no matter how close, means it's not absolutely certain.
MISTAKE: Thinking that a sure event means there's only one possible outcome in the sample space. | CORRECTION: A sure event means ALL possible outcomes in the sample space are favourable outcomes for that event. The sample space can have many outcomes.
MISTAKE: Calculating the probability of a sure event as 0. | CORRECTION: The probability of a sure event is always 1. A probability of 0 represents an Impossible Event.
Practice Questions
Try It Yourself
QUESTION: A spinner has sections numbered 1 to 5. What is the probability of the spinner landing on a number less than 6? | ANSWER: The numbers less than 6 are 1, 2, 3, 4, 5. All 5 outcomes are favourable. Total outcomes are 5. So, probability = 5/5 = 1.
QUESTION: In a standard deck of 52 playing cards, what is the probability of drawing a card that is either a heart, diamond, club, or spade? | ANSWER: A standard deck only contains hearts, diamonds, clubs, and spades. So, all 52 cards are favourable outcomes. Probability = 52/52 = 1.
QUESTION: A bag contains 10 blue pens and 5 black pens. If you pick a pen, what is the probability that it is NOT a red pen? | ANSWER: The pens in the bag are either blue or black. There are no red pens. So, picking a pen that is not red is a sure event because any pen you pick (blue or black) will satisfy the condition. Total pens = 15. Number of non-red pens = 15. Probability = 15/15 = 1.
MCQ
Quick Quiz
Which of the following describes a Sure Event?
An event that might happen
An event with a probability of 0
An event that is guaranteed to happen
An event with a probability of 0.5
The Correct Answer Is:
C
A Sure Event is defined as an event that is certain or guaranteed to happen, making its probability 1. Option B describes an Impossible Event, and Options A and D describe events that are not certain.
Real World Connection
In the Real World
Think about online payment systems like UPI. When you complete a transaction, it's a sure event that the money will either reach the recipient or be returned to you. There's no third outcome where the money just vanishes into thin air. This certainty is built into the system to ensure trust and reliability for millions of users daily.
Key Vocabulary
Key Terms
Probability: The chance of an event happening | Event: A set of outcomes from an experiment | Sample Space: All possible outcomes of an experiment | Impossible Event: An event that cannot happen, with probability 0 | Outcome: A single result of an experiment
What's Next
What to Learn Next
Now that you understand Sure Events, you're ready to explore Impossible Events and then delve into the general concept of Probability. These concepts will help you analyze uncertain situations and make informed decisions, just like data scientists do!
