Long-Run Chance and the Addition Rule

Name: Long-Run Chance and the Addition Rule
Author: StemPy Lab

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.

3 lessons, about 1 h 20 min3 simulations10 problems3 practice questionsPython in every lesson

Course outline (3 lessons)

Lesson 1about 25 min
Probability from data and from equal chances
There are two common ways to put a number on a chance. Count what happened in a record and divide by the number of tries, which gives a relative frequency. Or count equally likely outcomes, as for a fair die. This lesson shows when each way fits and how a set of probabilities must add up to $1$ .
1 simulation1 practice question1 Python program3 problems
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Lesson 2about 30 min
The law of large numbers by simulation
Toss a coin ten times and the share of heads can be far from a half. Toss it a hundred thousand times and the share is very close. This settling down is the law of large numbers. This lesson watches it happen in a simulation, measures how fast the share settles and shows what the law does not promise.
1 simulation1 practice question1 Python program3 problems1 Python lab
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Lesson 3about 25 min
Complements, exclusive events and the addition rule
Some chances are easier to find from what does not happen: $P(\text{not } A) = 1 - P(A)$ . Two events that cannot happen together simply add. Two events that can overlap need the addition rule, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ , which a Venn diagram makes clear.
1 simulation1 practice question1 Python program4 problems1 Python lab1 question set1 note
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15 questions · 20 min

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