Statistics & Data Science, Mathematics
High School (9–10)
High School (11–12)
Undergraduate
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Statistics Basics › Probability and ChanceStatistics Basics › Tables and GraphsChapter 3Probability Rules
A bus is late on some days and on time on others.
- A coin lands heads five times in a row.
- A game at a fair costs a coin to play.
- How likely is each thing, and what happens in the long run?
- This chapter finds probabilities from data and from equal chances, and checks every rule with a simulation.
- You will add and multiply chances, draw probability trees, read two-way tables and work out whether a game is fair.
- The Python is short and explained line by line.
Part of Statistics & Data Science · Essentials (chapter 3)
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Long-Run Chance and the Addition Rule
A made-up record says the school bus was late on 21 of 75 days. Is that a probability? Learn to find a probability from data and from equally likely outcomes, and watch a simulation settle down as the number of tries grows. Then add chances with a Venn diagram, and use the complement when it is easier to count what does not happen.
Independence, Trees and Streaks
Two alarms guard one door. If each works most of the time, how likely is it that at least one rings? Learn when two chances can be multiplied, draw probability trees for draws with and without replacement, and see why a big population makes the two kinds of draw almost the same. Then meet the gambler's fallacy, and find out by simulation how long the streaks in a random sequence really are.