12.5 Tree Diagrams

• The counting principle states: If a first experiment can be conducted M distinct ways and a second experiment can e conducted N distinct ways, then the two experiments in that order can be conducted M×N distinct ways.
• All possible outcomes of an experiment is called the sample space.
• A single outcome is called a sample point
• We can explore a sample space with a tree diagram.
• We can perform an experiment with replacement which means after we select an item we put it back.
• We can perform an experiment without replacement which means after we select an item we do not put it back.
• Do problems P 766: 7, 9, 11, 12, 15, 19, 20

12.6 OR and AND problems

• P(at least 1) = 1-P(none)
• Or problems
• These problems involve one experiment, with two events.
• P(A or B) = P(A) + P(B) - P(A and B)
• Two events A and B are mutually exclusive if it is impossible for both events to occur simultaneously. P(A and B) = 0
• Do P 778 number 11, 18-20, 21-26
• And Problems:
• These problems involve two experiments with two events.
• P(A and B) = P(A) P(B), we assume that event A occurred when computing P(B)
• Do Problem 12, 27-34, 41, 65