What is Decision Under Risk?

S8-SA5-0050

Grade Level:

Class 4

AI/ML, Data Science, Research, Journalism, Law, any domain requiring critical thinking

Definition

What is it?

Decision Under Risk means making a choice when you know the possible outcomes and how likely each outcome is to happen. It's about choosing the best option when you can guess the chances of good or bad things happening.

Simple Example

Quick Example

Imagine you are deciding whether to carry an umbrella to school. You know it might rain (50% chance) or it might not (50% chance). If it rains and you have an umbrella, you stay dry. If it rains and you don't, you get wet. This is a decision under risk.

Worked Example

Step-by-Step

Let's say you want to buy a new cricket bat. There are two shops.
---Shop A offers a bat for Rs. 1000. It has a 90% chance of being very good and a 10% chance of being just okay.
---Shop B offers a bat for Rs. 800. It has a 60% chance of being very good and a 40% chance of being just okay.
---Step 1: For Shop A, the 'expected value' of quality is (0.90 * Very Good) + (0.10 * Just Okay). Let's say 'Very Good' gives you 10 points and 'Just Okay' gives 5 points. So, Shop A's quality points = (0.90 * 10) + (0.10 * 5) = 9 + 0.5 = 9.5 points.
---Step 2: For Shop B, quality points = (0.60 * 10) + (0.40 * 5) = 6 + 2 = 8 points.
---Step 3: Now consider the price. Shop A costs more but gives higher expected quality. Shop B costs less but gives lower expected quality.
---Step 4: If you want the best possible quality for your money, you might choose Shop A because 9.5 quality points are better than 8, even if it costs more. If you are very budget-conscious, you might choose Shop B.
---Answer: The decision depends on whether quality or price is more important to you, after considering the risks (chances of good/okay quality).

Why It Matters

This concept is crucial for fields like Data Science and AI, where computers make choices based on probabilities. It helps researchers understand outcomes and journalists explain complex situations, enabling better, more informed choices in many careers.

Common Mistakes

MISTAKE: Only looking at the best possible outcome and ignoring the chances of other outcomes. | CORRECTION: Always consider ALL possible outcomes and their likelihoods before making a decision.

MISTAKE: Confusing 'risk' with 'uncertainty' (where you don't even know the chances). | CORRECTION: Remember, 'risk' means you know the probabilities; 'uncertainty' means you don't know them.

MISTAKE: Believing that a high probability guarantees an outcome. | CORRECTION: A high probability means it's LIKELY, but not GUARANTEED. There's always a chance the less likely event could still happen.

Practice Questions

Try It Yourself

QUESTION: You have a 70% chance of getting an ice cream if you finish your homework, and a 30% chance of not getting one. What does the 70% represent? | ANSWER: The probability or likelihood of getting an ice cream.

QUESTION: Your friend offers you two games. Game 1: Win Rs. 50 with 80% chance, lose Rs. 10 with 20% chance. Game 2: Win Rs. 100 with 40% chance, lose Rs. 20 with 60% chance. Which game has a higher expected winning amount? (Hint: Calculate Expected Value = (Win Amount * Win Chance) + (Lose Amount * Lose Chance)) | ANSWER: Game 1: (50 * 0.80) + (-10 * 0.20) = 40 - 2 = Rs. 38. Game 2: (100 * 0.40) + (-20 * 0.60) = 40 - 12 = Rs. 28. Game 1 has a higher expected winning amount.

QUESTION: A farmer is deciding between planting wheat or rice. Wheat has a 70% chance of giving Rs. 10,000 profit and 30% chance of Rs. 2,000 profit. Rice has a 50% chance of giving Rs. 12,000 profit and 50% chance of Rs. 1,000 profit. Which crop has a higher expected profit? Show your calculation. | ANSWER: Wheat: (0.70 * 10000) + (0.30 * 2000) = 7000 + 600 = Rs. 7600. Rice: (0.50 * 12000) + (0.50 * 1000) = 6000 + 500 = Rs. 6500. Wheat has a higher expected profit.

MCQ

Quick Quiz

What is the key difference between 'Decision Under Risk' and simply making a choice?

Decision Under Risk means you don't know any outcomes.

Decision Under Risk means you know the possible outcomes and their probabilities.

Decision Under Risk means there are no bad outcomes.

Decision Under Risk means you always get what you want.

The Correct Answer Is:

Option B correctly defines Decision Under Risk, where you have information about both the outcomes and their chances. The other options describe situations that are not 'Decision Under Risk'.

Real World Connection

In the Real World

When you use a weather app like AccuWeather or IMD, it tells you the 'chance of rain' for your city. This percentage helps you decide if you need an umbrella or not. This is a daily example of making a decision under risk, using data provided by meteorologists.

Key Vocabulary

Key Terms

PROBABILITY: The chance of something happening, usually shown as a percentage or fraction. | OUTCOME: A possible result of a decision or event. | EXPECTED VALUE: The average outcome you would expect if you made the same decision many times. | RISK: The possibility of something bad happening, where the chances are known.

What's Next

What to Learn Next

Next, explore 'Decision Under Uncertainty'. This will teach you how to make choices when you don't even know the probabilities of different outcomes, which is a common situation in real life. It builds on understanding risk.