AP STATISTICS Section 6.2 Probability Models. Objective: To be able to understand and apply the rules for probability. Random: refers to the type of order.

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AP STATISTICS Section 6.2 Probability Models

Objective: To be able to understand and apply the rules for probability. Random: refers to the type of order that reveals itself after a large number of trials. Probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions. Types of Probability: 1. Empirical: probability based on observation. Ex. Hershey Kisses:

2. Theoretical: probability based on a mathematical model. Ex. Calculate the probability of flipping 3 coins and getting all head. Sample Space: set of all possible outcomes of a random phenomenon. Outcome: one result of a situation involving uncertainty. Event: any single outcome or collection of outcomes from the sample space.

Methods for Finding the Total Number of Outcomes: 1. Tree Diagrams: useful method to list all outcomes in the sample space. Best with a small number of outcomes. Ex. Draw a tree diagram and list the sample space for the event where one coin is flipped and one die is rolled. 2. Multiplication Principle: If event 1 occurs M ways and event 2 occurs N ways then events 1 and 2 occur in succession M*N ways.

Ex. Use the multiplication principle to determine the number of outcomes in the sample space for when 5 dice are rolled. Sampling with replacement: when multiple items are being selected, the previous item is replaced prior to the next selection. Sampling without replacement: then the item is NOT replaced prior to the next selection.

IF EVENTS ARE DISJOINT, THEN THEY CAN NOT BE INDEPENDENT!!!!! Ex. Let A = earn an A in Statistics; P(A) = 0.30 Let B = earn a B in Statistics; P(B) = 0.40 Are events A and B disjoint? Are events A and B independent?

Independence vs. Disjoint Case 1) A and B are NOT disjoint and independent. Suppose a family plans on having 2 children and the P(boy) = 0.5 Let A = first child is a boy. Let B = second child is a boy Are A and B disjoint? Are A and B independent? (check mathematically)

Case 2) A and B are NOT disjoint and dependent. (Use a Venn Diagram for Ex) Are A and B disjoint? Are A and B independent? (check mathematically)

Case 3) A and B are disjoint and dependent. Given P(A) = 0.2, P(B) = 0.3 and P(A and B) = 0 Are A and B independent? (check mathematically) (Also refer to example for grade in class) Case 4) A and B are disjoint and independent. IMPOSSIBLE

Ex. Given the following table of information regarding meal plan and number of days at a university: A student is chosen at random from this university, find P(plan A)P(5 days) P(plan B and 2 days)P(plan B or 2 days) Are days and meal plan independent? (verify mathematically) Day/MealPlan APlan BTotal: Total: