What is Equally Likely Outcomes?

S7-SA3-0420

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 outcomes are results of an experiment that have the same chance of happening. This means no outcome is preferred or more probable than any other, given the conditions.

Simple Example

Quick Example

Imagine you are flipping a perfectly balanced coin. There are two possible outcomes: Heads or Tails. Since the coin is balanced, the chance of getting Heads is exactly the same as the chance of getting Tails. Both outcomes are equally likely.

Worked Example

Step-by-Step

Problem: A standard six-sided dice is rolled. Are the outcomes of getting a '1', '2', '3', '4', '5', or '6' equally likely?

Step 1: Identify all possible outcomes when rolling a standard six-sided dice. The outcomes are {1, 2, 3, 4, 5, 6}.
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Step 2: Consider if the dice is 'fair' or 'unbiased'. A standard dice is assumed to be fair, meaning each side has an equal chance of landing face up.
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Step 3: Determine the probability for each individual outcome. For a fair six-sided dice, the probability of rolling a '1' is 1/6. The probability of rolling a '2' is 1/6, and so on for all numbers up to '6'.
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Step 4: Compare the probabilities. Since P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = 1/6, all outcomes have the same probability.
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Answer: Yes, the outcomes of getting a '1', '2', '3', '4', '5', or '6' when rolling a standard six-sided dice are equally likely.

Why It Matters

Understanding equally likely outcomes is fundamental in many fields, from predicting cricket match results to designing safe self-driving cars. Engineers use this concept to ensure fairness in systems, while data scientists in AI/ML rely on it to build unbiased models. It's a core idea for careers in technology and research.

Common Mistakes

MISTAKE: Assuming outcomes are equally likely just because they are different. | CORRECTION: Always check if each outcome has the exact same probability of occurring. For example, in a biased coin, Heads and Tails are not equally likely.

MISTAKE: Confusing 'possible outcomes' with 'equally likely outcomes'. | CORRECTION: While all equally likely outcomes are possible, not all possible outcomes are equally likely. For instance, in a lottery, winning is possible, but not equally likely as losing.

MISTAKE: Ignoring the 'fairness' or 'bias' of the experiment setup. | CORRECTION: Always assume a fair setup (like a fair coin or dice) unless stated otherwise. If there's a bias (e.g., a loaded dice), outcomes will not be equally likely.

Practice Questions

Try It Yourself

QUESTION: In a bag, there are 5 red balls and 5 blue balls. If you pick one ball without looking, are the outcomes of picking a red ball or a blue ball equally likely? | ANSWER: Yes

QUESTION: A spinner has 4 sections: Red, Blue, Green, and Yellow. The Red section is half the size of the Blue, Green, and Yellow sections, which are all equal. Are the outcomes of landing on Red, Blue, Green, or Yellow equally likely? | ANSWER: No

QUESTION: You have a deck of 52 playing cards. If you draw one card, are the outcomes of drawing a 'King' or drawing an 'Ace' equally likely? Explain why. | ANSWER: Yes, because there are 4 Kings and 4 Aces in a standard deck, so the probability of drawing a King (4/52) is the same as drawing an Ace (4/52).

MCQ

Quick Quiz

Which of these scenarios involves equally likely outcomes?

Winning a lottery ticket versus losing it.

Rolling a '6' on a fair six-sided dice versus rolling any other number.

Drawing a heart card versus drawing a spade card from a shuffled deck.

Guessing the correct answer on a multiple-choice question with 4 options if you don't know the answer.

The Correct Answer Is:

Option C is correct because a standard deck has 13 heart cards and 13 spade cards, making their probabilities of being drawn equal (13/52 each). Other options involve unequal probabilities.

Real World Connection

In the Real World

Equally likely outcomes are crucial in making fair decisions. For example, when an umpire uses a coin toss to decide which team bats first in a cricket match, they rely on the coin having equally likely outcomes (Heads or Tails) to ensure fairness. This concept is also used in secure online payment systems like UPI to ensure random and unbiased generation of transaction IDs.

Key Vocabulary

Key Terms

OUTCOME: A possible result of an experiment or event. | PROBABILITY: The measure of how likely an event is to occur. | FAIR: Unbiased; not favoring one outcome over another. | EXPERIMENT: A procedure carried out to support, refute, or validate a hypothesis.

What's Next

What to Learn Next

Now that you understand equally likely outcomes, you're ready to explore 'Theoretical Probability'. This concept builds directly on what you've learned, showing you how to calculate the exact probability of events when outcomes are equally likely. Keep up the great work!