Probability Basics in 5 Minutes — Free Quick Revision

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TL;DR: Learn Probability Basics in about 5 minutes — a free bite-sized module with a clear explanation, a worked example and a quick quiz for Indian students…

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Probability = (favorable outcomes) / (total outcomes). Always between 0 and 1. P(certain) = 1, P(impossible) = 0.

Maths · Class 9 · about 6 minutes

The Idea

Probability measures how likely something is to happen. It's a number between 0 and 1 (or 0% to 100%).

P(Event) = (Number of favorable outcomes) / (Total number of possible outcomes)

Examples: - A fair die has 6 faces. P(rolling a 3) = 1/6 ≈ 0.167 or 16.7%. - A coin has 2 sides. P(heads) = 1/2 = 0.5 or 50%. - If there are 10 red and 5 blue balls in a bag, P(drawing red) = 10/15 = 2/3.

Key rules: - P(Event) = 0 → impossible (will never happen) - P(Event) = 1 → certain (will definitely happen) - P(Event A) + P(not A) = 1 - P(A and B) = P(A) × P(B) if A and B are independent

Probability is used in weather forecasts, insurance, gambling, and every decision involving uncertainty.

Worked Example: Bag of Colored Balls

Problem. A bag contains 3 red, 4 green, and 5 blue balls. If you draw one ball randomly, what is the probability it is green?

Solution.

Total balls = 3 + 4 + 5 = 12 Favorable outcomes (green) = 4 Probability = 4/12 = 1/3 ≈ 0.333 or 33.3%

There's a 1 in 3 chance of drawing green.

Quick Quiz

Answer each one before reading the explanation beneath it.

1. A standard deck has 52 cards (4 suits, 13 ranks). What is P(drawing a King)?

• 1/13 — correct
• 1/52
• 4/13
• 1/4

1/13

2. If P(rain tomorrow) = 0.3, what is P(no rain)?

• 0.3
• 0.7 — correct
• 0.5
• Cannot be determined

0.7

3. You flip a fair coin twice. What is P(both heads)?

• 1/2
• 1/4 — correct
• 1/3
• 2/3

1/4

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