What are Equally Likely Events?

S7-SA3-0309

Grade Level:

Class 12

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

Definition

What is it?

Equally likely events are outcomes of an experiment that have the same chance of happening. This means no single outcome is expected to occur more often than any other, given the same conditions.

Simple Example

Quick Example

Imagine you are flipping a perfectly balanced coin. The chance of getting 'Heads' is the same as the chance of getting 'Tails'. Both outcomes are equally likely.

Worked Example

Step-by-Step

Let's say your teacher is picking one student randomly from a class of 30 boys and 20 girls to represent the class in an inter-school debate.

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Step 1: Identify the total number of students in the class. Total students = 30 boys + 20 girls = 50 students.

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Step 2: Consider the event of picking a boy. The number of boys is 30.

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Step 3: Consider the event of picking a girl. The number of girls is 20.

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Step 4: Are these events equally likely? No, because the number of boys (30) is not equal to the number of girls (20).

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Step 5: Now, let's consider a different scenario: picking any specific student (e.g., Rohan) versus picking any other specific student (e.g., Priya). Each specific student has 1 chance out of 50 of being picked.

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Answer: Picking a boy and picking a girl are NOT equally likely events in this scenario. However, picking any one specific student (like Rohan) is equally likely as picking any other specific student (like Priya), both having a 1/50 chance.

Why It Matters

Understanding equally likely events is crucial for making fair decisions and predicting outcomes in many fields. For example, in AI/ML, it helps create unbiased models; in FinTech, it's used to assess risk fairly; and in Physics, it helps analyze particle behavior. This concept lays the foundation for careers in data science, engineering, and even medicine.

Common Mistakes

MISTAKE: Assuming all outcomes are equally likely in every situation. | CORRECTION: Always check if each outcome truly has the same number of possibilities or conditions for it to occur.

MISTAKE: Confusing 'equally likely' with 'having a 50-50 chance'. | CORRECTION: 'Equally likely' means all outcomes have the same probability, not necessarily 1/2. If there are 4 equally likely outcomes, each has a 1/4 chance.

MISTAKE: Not considering all possible outcomes in an experiment. | CORRECTION: Before deciding if events are equally likely, list down ALL possible outcomes in the sample space.

Practice Questions

Try It Yourself

QUESTION: You have a bag with 5 red marbles and 5 blue marbles. If you pick one marble without looking, is picking a red marble equally likely as picking a blue marble? | ANSWER: Yes

QUESTION: A standard six-sided dice is rolled. Is rolling a '1' equally likely as rolling an 'even number'? | ANSWER: No. Rolling a '1' has 1 outcome, while rolling an 'even number' (2, 4, 6) has 3 outcomes.

QUESTION: In a lottery, there are 100 tickets, numbered 1 to 100. If one ticket is drawn randomly, is the event of drawing a ticket with a number less than 10 equally likely as drawing a ticket with a number greater than 90? | ANSWER: No. Numbers less than 10 are (1, 2, ..., 9) - 9 outcomes. Numbers greater than 90 are (91, 92, ..., 100) - 10 outcomes. They are not equally likely.

MCQ

Quick Quiz

Which of these is an example of equally likely events?

Drawing a King from a deck of cards vs. drawing any other card.

Rolling a 3 on a fair six-sided die vs. rolling a 5 on the same die.

Winning a cricket match vs. losing a cricket match.

It raining tomorrow vs. it not raining tomorrow.

The Correct Answer Is:

When rolling a fair six-sided die, each face (1, 2, 3, 4, 5, 6) has an equal 1/6 chance of appearing. So, rolling a 3 has the same probability as rolling a 5. Other options involve unequal probabilities or external factors.

Real World Connection

In the Real World

When you use a food delivery app like Swiggy or Zomato, the system often assigns delivery partners. If there are multiple delivery partners equally close and available, the system might pick one randomly, treating each as an equally likely choice to ensure fairness and efficiency. This concept is also used in creating fair games or lotteries.

Key Vocabulary

Key Terms

PROBABILITY: The chance of an event happening. | OUTCOME: A possible result of an experiment. | EXPERIMENT: A process that results in one of several possible outcomes. | SAMPLE SPACE: The set of all possible outcomes of an experiment. | FAIR: Unbiased; not favoring any particular outcome.

What's Next

What to Learn Next

Now that you understand equally likely events, you're ready to explore 'Probability of an Event'. This next topic will show you how to calculate the actual chance of specific equally likely events happening, which is super useful!