Introduction to Probability

Learn the fundamental concepts of probability, including definitions, formulas, and real-life examples.

🎲 What is Probability?

Probability is a branch of mathematics that deals with uncertainty. It tells us how likely something is to happen.

In simple terms:

Probability is a number between 0 and 1 that shows how likely an event is to occur.

  • If something is impossible, its probability is 0. If something is certain, its probability is 1.

🔢 Probability Formula

If all outcomes are equally likely, the probability of an event happening is:

P(E)=Number of favorable outcomesTotal number of possible outcomesP(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

🧠 Example 1: Tossing a Coin

A coin has 2 sides: Heads (H) and Tails (T).

  • What’s the probability of getting a Head?
P(Head)=12P(\text{Head}) = \frac{1}{2}
  • What’s the probability of getting a Tail?
P(Tail)=12P(\text{Tail}) = \frac{1}{2}

🎲 Example 2: Rolling a Die

A die has 6 faces numbered 1 to 6.

  • What’s the probability of rolling a 3?
P(3)=16P(3) = \frac{1}{6}
  • What’s the probability of rolling a number less than 5?

Numbers less than 5: 4 → 4 outcomes

P(less than 5)=46=23P(\text{less than 5}) = \frac{4}{6} = \frac{2}{3}

🧩 Key Vocabulary

Term

Meaning

Experiment

An action with an uncertain result (e.g., rolling a die)

Outcome

A possible result of an experiment (e.g., getting a 6)

Event

A set of one or more outcomes

Sample Space (S)

The set of all possible outcomes

For example, when rolling a die:

S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}

Fact

If you toss two coins, the sample space becomes:

S={HH,HT,TH,TT}S = \{HH, HT, TH, TT\}

Each pair has equal chance. So:

P(Exactly one head)=24=12P(\text{Exactly one head}) = \frac{2}{4} = \frac{1}{2}

Summary

  • Probability helps us reason about uncertain outcomes.
  • It always lies between 0 and 1.
  • Use the formula P(E)=favorable outcomestotal outcomesP(E) = \frac{\text{favorable outcomes}}{\text{total outcomes}} when outcomes are equally likely.
  • Real-life applications include games, weather forecasts, and risk assessments.

Keep exploring — probability is all around you! 🎯

Required Exercise • an-Id

FILL
⏳ 0:05 min
❓ 5 Questions
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🗓 Taken on Jul 5, 2025

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