Tree Diagrams

• The Counting Principle states that if one experiment has M outcomes and a second experiment has N outcomes then the two experiments together have M×N outcomes.
• If I roll a die, then toss a coin, there are 6×2 or 12 outcomes.
• The list of all outcomes is called the sample space.
• A single outcome is called a sample point
• Tree diagrams are useful to determine the sample space.
• Draw the tree diagram for the die/coin experiment.
• If we perform an experiment twice, and the result of the first experiment is available for the second experiment, this is called with replacement otherwise it is called without replacement
• P(event happening at least once) = 1-P(event does not happen)
• Do problems 7, 9, 11, 19

And and Or Problems

• Problems like "Roll a die, what is the probability that the result is an even number or greater than 4"
• P(A or B) = P(A) + P(B) - P(A and B)
• This is just a Venn diagram problem.
• Problem number 35, 37
• Problems like Select two cards from the deck, what is the probability that one is a queen and the other is an ace?
• P(A and B) = P(A) &timies; P(B)
• This assumes A occurs then B occurs
• Dependent vs Independent events.
• Problem 27, 29, 31