SECTION 4.2 SUMMARY

• • A probability model for a random phenomenon consists of a sample space S and an assignment of probabilities P.

• • The sample space S is the set of all possible outcomes of the random phenomenon. Sets of outcomes are called events. P assigns a number P(A) to an event A as its probability.

• • The complement A^c of an event A consists of exactly the outcomes that are not in A. Events A and B are disjoint if they have no outcomes in common. Events A and B are independent if knowing that one event occurs does not change the probability we would assign to the other event.

• • Any assignment of probability must obey the rules that state the basic properties of probability:

  • Rule 1. 0 ≤ P(A) ≤ 1 for any event A.

  • Rule 2. P(S) = 1.

  • Rule 3. Addition rule: If events A and B are disjoint, then P(A or B) = P(A) + P(B).

  • Rule 4. Complement rule: For any event A, $P\left(A^C\right)=1-P\left(A\right)$.

  • Rule 5. Multiplication rule: If events A and B are independent, then P(A and B) = P(A)P(B).