Chapter Summary
The collection of all possible outcomes forms the sample space S. An event is a subset of the sample space. The probability of an event is the long-run relative frequency of the event. The Law of Large Numbers guarantees that the relative frequency of an event in data that lack patterns converges to the probability of the event in the long run. Several rules allow us to manipulate probabilities. If A and B are events, then
| 1. Something must happen | P(S) = 1 |
| 2. Probabilities lie between 0 and 1 | 0 ≤ P(A) ≤ 1 |
| 3. Addition Rule | P(A or B) = P(A) + P(B) − P(A and B) = P(A) + P(B) if A and B are disjoint |
| 4. Complement Rule | P(A) = 1 − P(Ac) |
5. Multiplication Rule for Independent Events |
P(A and B) = P(A) × P (B) |
Independence ...
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