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Basic Probability

Overview

What are the odds?

What is it?

A fraction representing the likelihood of an event occurring: (Part / Whole).

History

Pascal used this to calculate how to divide the pot of an unfinished gambling game fairly.

Key Idea

OR means Add (+). AND means Multiply (*).

Practice This Topic

Concept Guide

Plain English: Probability is just counting. The top number is 'Good Outcomes' (what you want). The bottom number is 'Total Possible Outcomes'. It's always a decimal between 0 and 1.

Real-world example: Insurance. Companies calculate the probability of you crashing your car to set your price.

How to do it

  1. Count the number of 'Success' outcomes.
  2. Count the 'Total' number of possible outcomes.
  3. Write as a fraction: Success / Total.
  4. Convert to % by multiplying by 100.
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Common Pitfall

The Gambler's Fallacy. Thinking a coin is 'due' to hit Heads after 5 Tails. The coin has no memory. It's always 50%.

Word Problem
"A jar has 3 red marbles and 7 blue marbles. What is the probability of picking red?"
Reasoning: Successes (Red) = 3. Total Marbles = 10. Probability = 3/10 or 30%.

Practice Examples

Coin Flip
Heads: 1/2 Tails: 1/2
Total must sum to 1.