SECTION 4.2 Summary

• A probability model for a random phenomenon consists of a sample space and an assignment of probabilities .
• The sample space is the set of all possible outcomes of the random phenomenon. Sets of outcomes are called events. assigns a number to an event as its probability.
• The complement of an event consists of exactly the outcomes that are not in .
• Events and are disjoint if they have no outcomes in common.
• Events and 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. for any event .
  • Rule 2. .
  • Rule 3. Addition rule: If events and are disjoint, then .
  • Rule 4. Complement rule: For any event , .
  • Rule 5. Multiplication rule: If events and are independent, then .