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What is a Sure Event's Probability?
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 is an event that is certain to happen. Its probability is a measure of how likely it is for that event to occur, and for a sure event, this likelihood is the highest possible.
Simple Example
Quick Example
Imagine you have a bag full of only red ladoos. If you pick a ladoo from the bag, it is absolutely certain that you will pick a red ladoo. This is a sure event.
Worked Example
Step-by-Step
Let's find the probability of getting a number less than 7 when rolling a standard six-sided dice.
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Step 1: Identify all possible outcomes when rolling a dice. The possible outcomes are {1, 2, 3, 4, 5, 6}. The total number of outcomes is 6.
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Step 2: Identify the outcomes that satisfy the event "getting a number less than 7". These outcomes are {1, 2, 3, 4, 5, 6}. The number of favourable outcomes is 6.
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Step 3: Recall the formula for probability: Probability = (Number of favourable outcomes) / (Total number of possible outcomes).
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Step 4: Substitute the values into the formula: Probability = 6 / 6.
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Step 5: Calculate the probability: Probability = 1.
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Answer: The probability of getting a number less than 7 when rolling a standard six-sided dice is 1.
Why It Matters
Understanding sure events helps scientists and engineers predict outcomes with certainty, which is crucial in fields like AI/ML for building reliable systems or in medicine for ensuring drug safety. Doctors and software developers use this concept to make sure critical systems work without fail.
Common Mistakes
MISTAKE: Thinking a sure event has a probability of 0. | CORRECTION: A probability of 0 means an event is impossible. A sure event is certain, so its probability is 1.
MISTAKE: Confusing a 'very likely' event with a 'sure' event. | CORRECTION: A 'very likely' event might have a probability like 0.99, but it's not 1. A sure event MUST have a probability of exactly 1.
MISTAKE: Expressing the probability of a sure event as a percentage greater than 100%. | CORRECTION: Probability is always between 0 and 1 (or 0% and 100%). A sure event has a probability of 1 or 100%.
Practice Questions
Try It Yourself
QUESTION: What is the probability that the sun will rise tomorrow? | ANSWER: 1
QUESTION: A box contains 10 blue pens. What is the probability of picking a blue pen from the box? | ANSWER: 1
QUESTION: If you have a bag with 5 red marbles and 5 blue marbles, what is the probability of picking a marble that is either red or blue? Show your steps. | ANSWER: Probability = (Number of (red or blue) marbles) / (Total marbles) = 10 / 10 = 1.
MCQ
Quick Quiz
Which of the following is true about the probability of a sure event?
It is 0
It is 0.5
It is 1
It is greater than 1
The Correct Answer Is:
C
A sure event is certain to happen, meaning it has the highest possible probability, which is 1. A probability of 0 means an event is impossible.
Real World Connection
In the Real World
When you use a reliable UPI app like Google Pay or PhonePe, the probability of your payment being processed correctly (assuming good network and sufficient balance) is designed to be very close to 1. Engineers writing the code for these apps work to ensure that critical transactions are sure events, preventing issues in real-time payments across India.
Key Vocabulary
Key Terms
SURE EVENT: An event that is certain to happen. | PROBABILITY: A measure of the likelihood of an event occurring. | OUTCOME: A possible result of an experiment. | CERTAIN: Absolutely sure or positive.
What's Next
What to Learn Next
Now that you understand sure events, you can explore impossible events, which have a probability of 0. Then, you can move on to understanding how to calculate probabilities for events that are neither sure nor impossible, which is where most real-world problems lie!
