What is Favourable Outcomes?

S3-SA3-0067

Grade Level:

Class 8

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Favourable outcomes are the specific results you want to happen from a random experiment. They are the outcomes that satisfy a particular condition or event you are interested in. In simple terms, it's what you're hoping to get!

Simple Example

Quick Example

Imagine you are playing Ludo and want to roll a '6' to get your piece out of the home. In this situation, rolling a '6' is your favourable outcome. All other numbers (1, 2, 3, 4, 5) are not favourable for that specific goal.

Worked Example

Step-by-Step

Let's say a cricket team wants to win the toss. There are two possible outcomes when tossing a coin: Heads or Tails. If the captain calls 'Heads', then getting 'Heads' is the favourable outcome for them.
---Step 1: Identify the experiment. The experiment is tossing a coin.
---Step 2: List all possible outcomes. The possible outcomes are {Heads, Tails}.
---Step 3: Identify what the team wants. The team wants to win the toss by calling 'Heads'.
---Step 4: Determine the outcome that matches what the team wants. The outcome 'Heads' matches what they want.
---Answer: So, the number of favourable outcomes for the team to win the toss by calling 'Heads' is 1 (getting Heads).

Why It Matters

Understanding favourable outcomes is super important for predicting events and making smart decisions, just like how weather apps predict rain or how doctors assess health risks. Engineers use this to design safer bridges, and data scientists use it to understand customer behaviour for apps like Flipkart or Swiggy.

Common Mistakes

MISTAKE: Confusing favourable outcomes with all possible outcomes. | CORRECTION: Favourable outcomes are ONLY the ones you want, while possible outcomes are ALL the things that can happen.

MISTAKE: Forgetting to count specific items when finding favourable outcomes. | CORRECTION: Always count how many times your desired outcome can occur, even if it's the same 'type' of outcome.

MISTAKE: Not clearly defining the 'event' or 'condition' for which outcomes are favourable. | CORRECTION: Before counting, clearly state what you are looking for (e.g., 'rolling an even number', 'picking a red ball').

Practice Questions

Try It Yourself

QUESTION: You have a bag with 5 red marbles and 3 blue marbles. What are the favourable outcomes if you want to pick a red marble? | ANSWER: Picking any of the 5 red marbles.

QUESTION: In a class of 30 students, 12 play football, 10 play basketball, and 8 play neither. If you randomly pick a student, what are the favourable outcomes for picking a student who plays football? | ANSWER: Picking any of the 12 students who play football.

QUESTION: A spinner has sections numbered 1, 2, 3, 4, 5, 6, 7, 8. What are the favourable outcomes for spinning a number greater than 5 AND an even number? | ANSWER: Spinning a 6 or an 8. (Numbers greater than 5 are 6, 7, 8. Among these, even numbers are 6, 8).

MCQ

Quick Quiz

You roll a standard six-sided dice. What are the favourable outcomes if you want to roll an odd number?

{2, 4, 6}

{1, 2, 3, 4, 5, 6}

{1, 3, 5}

{3, 5}

The Correct Answer Is:

Favourable outcomes are the ones that meet the condition. Odd numbers on a dice are 1, 3, and 5. Options A and D are incomplete or incorrect, and B lists all possible outcomes, not just the favourable ones.

Real World Connection

In the Real World

When you book a train ticket on IRCTC, the system calculates the probability of getting a confirmed seat based on available berths and past booking trends. 'Getting a confirmed seat' is the favourable outcome for you. Similarly, when a food delivery app like Zomato predicts delivery time, it's calculating the chances of a 'fast delivery' (a favourable outcome for you) based on traffic, restaurant prep time, etc.

Key Vocabulary

Key Terms

OUTCOME: A possible result of an experiment | EXPERIMENT: A process with well-defined results | EVENT: A collection of one or more outcomes | PROBABILITY: The chance of a favourable outcome happening

What's Next

What to Learn Next

Now that you know what favourable outcomes are, the next step is to learn about 'Total Number of Outcomes'. Combining these two concepts will help you understand 'Probability', which tells you how likely your desired event is to happen. Keep up the great work!