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🎲 Probability

Measure chance with confidence: from coin flips to conditional reasoning.

lessons

~30 min

to learn

🔢 Math

subject

Teens

level

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What you’ll learn

Compute basic probabilities from sample spaces and use complements and odds.Probability is favorable outcomes over total outcomes, from 0 to 1. Listing the sample space, using complements, and distinguishing odds from probability are the core basics.
Apply the multiplication and addition rules and distinguish independent from dependent events.Independent events multiply and have no memory, dispelling the gambler's fallacy. Dependent events update after each draw, and the addition rule handles or-events, accounting for overlap.
Use conditional probability, expected value, and the law of large numbers.Conditional probability updates with new evidence, expected value gives the long-run average, and the law of large numbers explains why averages stabilize over many trials.

Questions this course answers

What is the probability of rolling a 4 on a standard six-sided die?

There is one favorable outcome out of six equally likely faces, so 1/6.

If the probability of rain is 0.3, the probability of no rain is:

An event and its complement sum to 1, so 1 - 0.3 = 0.7.

How many outcomes are in the sample space of flipping two coins?

The outcomes are HH, HT, TH, and TT, so there are 4.

For two independent events, the probability both occur is found by:

For independent events, multiply the individual probabilities.

After five heads in a row on a fair coin, the chance of heads next is:

Flips are independent; the coin has no memory, so it stays 1/2.

Drawing marbles without replacing them creates events that are:

Not replacing changes later probabilities, making the events dependent.

Grounded in trusted sources

Conditional Probability and Independent Events, Statistics LibreTexts, https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/03:_Basic_Concepts_of_Probability/3.03:_Conditional_Probability_and_Independent_Events
Law of large numbers, Wikipedia, https://en.wikipedia.org/wiki/Law_of_large_numbers
Conditional probability, Wikipedia, https://en.wikipedia.org/wiki/Conditional_probability
Introductory Statistics, OpenStax (Illowsky & Dean, 2018), https://openstax.org/details/books/introductory-statistics
Probability, Khan Academy, https://www.khanacademy.org/math/statistics-probability/probability-library

Every Wunder lesson is built from real, reputable sources — never invented.

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