Count equally likely outcomes
Keep outcomes equally likely before dividing favorable cases by all cases.
Goes with Reason with probability
Probability
Count outcomes, update chances with new information, and compare decisions through worked examples.
12 lessons
Lessons
Decide whether order matters
Separate an ordered arrangement from a group that contains the same items.
Goes with Counting combinations
Condition on information
Use natural counts to choose the right conditional denominator.
Goes with Conditional probability
Update after a draw
Track the changing counts when an object is not replaced.
Goes with Conditional probability
Follow the host rule
Explain why the same empty door can lead to different odds.
Goes with Switch or stay
Compare expected rewards
Subtract the cost and weight every net outcome by its probability.
Goes with Risk and reward
Count winning sequences
Use complements and disjoint cases to compare multi-roll targets.
Goes with Risk and reward
Count birthday collisions
Use the chance of no match to understand why shared birthdays arrive surprisingly soon.
Goes with Birthday collisions
Why patterns overlap
Separate a pattern’s chance in one window from the time you wait for it.
Goes with Pattern races
Race patterns with a biased coin
Track both patterns on one sequence and count unfinished races.
Goes with Pattern races
Compare dice in pairs
Discover why a die can beat one rival and lose to another.
Goes with Nontransitive dice
Choose a die after two rolls
Build the distribution of sums before choosing a counter to an opponent.
Goes with Nontransitive dice
Ready to try?
Take a method into a practice, or discover something new.
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