Probability

1) Hook — A Fun Real-Life Example

Imagine you and your friends are playing a game of Ludo on a rainy evening in Mumbai. You roll a fair six-faced dice and wonder: What is the chance that you will get a 6 and move your token forward? This simple question introduces us to the exciting world of Probability, which helps us measure how likely an event is to happen.

2) Core Concepts

What is Probability?

Probability is the measure of the likelihood of an event occurring. It is a number between 0 and 1, where:

• 0 means the event will never happen.
• 1 means the event will always happen.

Sample Space (S): The set of all possible outcomes of an experiment.

Event (E): A subset of the sample space, whose probability we want to find.

Example 1: Tossing a fair coin once.

Probability of getting Heads, P(Heads) = Number of favourable outcomes / Total outcomes = 1/2

Example 2: Drawing a card from a well-shuffled Indian deck of 52 cards and finding the probability of getting a King.

Number of Kings = 4

Probability of King, P(King) = 4/52 = 1/13

3) Key Formulas / Rules

4) Did You Know?

Probability theory was first formalized by Indian mathematician Bhāskara II in the 12th century, centuries before it became a formal branch of mathematics in Europe! He used early ideas of chance and uncertainty in his works.

5) Exam Tips

• Always write the sample space first: It helps avoid mistakes in counting total outcomes.
• Check if the event is favourable or not: Carefully identify which outcomes are favourable.
• Remember the probability range: Probability cannot be negative or greater than 1.
• Use fractions in simplest form: Always reduce your answer to simplest fraction or decimal as per question.
• Common question pattern: "Find the probability of..." or "If an event is impossible/certain, what is its probability?"
• Watch for wording tricks: Words like "at least", "not", "complement" require careful interpretation.