3.1 Basics of Probability Probability = Chance of an outcome Probability experiment = action through which specific results (counts, measurements, responses) are obtained Outcome = result of 1 trial Sample space = set (list) of all possible outcomes Event = 1 or more outcomes, subset of sample space Simple event = only 1 outcome

Tree Diagrams Can be used to find sample space Think of POSSIBLE outcomes for each event. EX: How many outcomes are there AND what is the sample space of Flipping a coin AND then rolling a six sided die?

Example: How many outcomes are there AND what is the sample space for : answering a question on a survey (agree, disagree, no opinion) AND tossing a coin.

Are these events (E) simple? 1. You randomly select a computer chip from a batch produced that day. Event A is selecting a specific defective chip. 2. You roll a six sided die. Event B is rolling at least a You ask a student’s age. – A) event C is the student’s age is between 18 and 23 inclusive. – B) event D is the student’s age is 20.

Types of Probability

Examples: Classical What is the probability of: You roll a 6 sided die. – 1) Event A: rolling a 3 – 2) Event B: rolling a 7 – 3) Event C: rolling a number LESS THAN 5 You select a card from a deck of 52 (standard) – 1)Event D: selecting a 7 of diamonds – 2) Event E: selecting a diamond – 3) Event F: selecting a diamond, heart, club OR spade

Examples: Empirical What is the probability? 1. While fishing, the FREQUENCY of the times you caught 3 kinds of fish were 13 blugill, 17 redgill and 10 croppy. What is the probability that the next fish will be a bluegill? 2. Out of every 100 insurance claims, 4 are fraudulent. What is the probability the next claim will be fraudulent? 3. Try Example #5 and Try it yourself # 5 on p Try Example #6 and Tri it yourself # 6 on p. 109

Complement Complement of event E = all outcomes NOT included in the event  E’ : “E prime”  P(E) + P(E’) = 1  P(E) = 1 – P(E’)  P(E’) = 1 – P(E) In example #5, what is probability of the employee being NOT between 25 and 34? In example 4, what is the probability the next fish is NOT a redgill?