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What is the Sure Event?
Grade Level:
Class 8
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
A Sure Event (also called a Certain Event) is an event that will always happen, no matter what. Its probability is always 1, meaning it's 100% guaranteed to occur.
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 colour will it be? It will definitely be red! So, 'picking a red ladoo' is a Sure Event here.
Worked Example
Step-by-Step
Let's say you have a standard dice with faces numbered 1 to 6.
---STEP 1: Identify all possible outcomes when you roll the dice. The outcomes are {1, 2, 3, 4, 5, 6}.
---STEP 2: Consider the event 'rolling a number less than 7'.
---STEP 3: Check which outcomes satisfy this event. All numbers {1, 2, 3, 4, 5, 6} are less than 7.
---STEP 4: The number of favourable outcomes (rolling a number less than 7) is 6.
---STEP 5: The total number of possible outcomes is also 6.
---STEP 6: Calculate the probability: Probability = (Favourable Outcomes) / (Total Outcomes) = 6/6 = 1.
---ANSWER: Since the probability is 1, rolling a number less than 7 on a standard dice is a Sure Event.
Why It Matters
Understanding sure events is fundamental in fields like Data Science and AI, where predicting outcomes is key. Engineers use this concept to design systems that are certain to work under specific conditions, ensuring safety and reliability. Even in economics, certain market conditions are considered sure events.
Common Mistakes
MISTAKE: Thinking a highly likely event is a Sure Event. For example, 'the sun will rise tomorrow' is highly likely but not 100% mathematically sure due to extremely rare astronomical possibilities. | CORRECTION: A Sure Event must have a probability of exactly 1, meaning there is absolutely no possibility of it not happening.
MISTAKE: Confusing a Sure Event with an Impossible Event. | CORRECTION: A Sure Event has a probability of 1 (it always happens), while an Impossible Event has a probability of 0 (it never happens).
MISTAKE: Believing that a Sure Event means you know the exact outcome before it happens, even if there are multiple possibilities. | CORRECTION: A Sure Event means the event itself (e.g., 'getting a number less than 7') is guaranteed, even if the specific outcome (e.g., whether it's 1 or 2 or 3) is still random.
Practice Questions
Try It Yourself
QUESTION: If you have a bag with 10 green marbles, what is the probability of picking a green marble? Is it a Sure Event? | ANSWER: The probability is 10/10 = 1. Yes, it is a Sure Event.
QUESTION: You are checking your mobile phone for messages. Is 'receiving a message' a Sure Event? Explain why or why not. | ANSWER: No, it is not a Sure Event. While you might receive messages often, there's always a chance you might not receive any new messages at a particular moment (e.g., if no one sends you one, or if you have no network). Its probability is less than 1.
QUESTION: A spinner has sections numbered 1, 2, 3, 4, 5. What is the probability of the spinner landing on a number greater than 0? Is this a Sure Event? | ANSWER: All numbers (1, 2, 3, 4, 5) are greater than 0. So, favourable outcomes = 5, total outcomes = 5. Probability = 5/5 = 1. Yes, it is a Sure Event.
MCQ
Quick Quiz
Which of the following describes a Sure Event?
An event that is very likely to happen.
An event that has a probability of 0.
An event that is guaranteed to happen, with a probability of 1.
An event that might happen or might not happen.
The Correct Answer Is:
C
A Sure Event is defined as an event that is certain to occur, meaning its probability is exactly 1. Options A, B, and D describe events with probabilities other than 1 or uncertainty.
Real World Connection
In the Real World
When you book a train ticket using the IRCTC app, the event 'the booking system will try to process your request' is a Sure Event, assuming the system is operational. Or, if you open the weather app, the event 'the app will display some weather information' is a Sure Event, even if the forecast itself might change. This foundational understanding helps in building reliable software and systems.
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. | Impossible Event: An event that can never happen, with a probability of 0.
What's Next
What to Learn Next
Great job understanding Sure Events! Now that you know about events that are certain, you should explore 'Impossible Events'. This will help you understand the full range of probabilities, from 0 to 1, and make you a master of basic probability concepts.
