Section 3.1 Notes Basic Concepts of Probability

Probability Experiments A probability experiment is an action or trial through which specific results (counts, measurements or responses) are obtained. Outcome: is the result of a trial. Sample Space: the set of all possible outcomes of a probability experiment.

Example 1 A probability experiment consists of tossing a coin and then rolling a six sided die. Describe the sample space.

Example 2 A probability experiment consists of getting rolling a die and then pulling a card from a deck of 5 cards numbered 1 through 5. Describe the sample space.

Example 3 A probability experiment consists of recording responses to a survey, “There should be a limit on the amount of A’s in one class” (agree, disagree, no opinion) and the gender of the respondent.

Example 4 A probability experiment consists of recording responses to a survey, “There should be a limit on the amount of A’s in one class” (agree, disagree, no opinion) and the political party (Democrat, Republican or Other) of the respondent.

Notes 3.1 (Part 2) Simple Event and Classical Probability

Simple Event Different blood types A, B, AB, and O Probability (blood is type A): this is a simple event since you are only searching for one favorable outcome. Probability (blood is not type A): this is not a simple event since you are searching for three possible outcomes (B, AB, and O)

Example 5 For quality control, you randomly select a computer chip from a batch that was manufactured that day. Event A is selecting a specific defective chip. Is this event simple or not simple?

Example 6 You roll a six sided die, Event B is rolling at least a 4. Is the event simple or not simple?

Example 7 You ask for a student’s age at his or her last birthday. Decide whether each event is simple or not. Event C: the students age is between 18 and 23, inclusive. Event D: the students age is 20.

Types of probabilities Classical (or theoretical), Empirical (or statistical), and subjective probabilities.

Classical (or Theoretical) Probability Classical probability: is used when each outcome in a sample space is equally likely to occur. P (Event) = Number of outcomes of Event Total number of outcome in sample space

Example 8 You roll a six sided die. Find the probability of the following events. P (rolling a 3) P (rolling a 7) P (rolling a number less than 5)

Warm Up A company is selecting employees for a drug test. The company uses a computer to generate randomly employee number that range from 1 – 751 a)Probability of selecting a number less than 200 b)Probability of selecting a number divisible by 50.

Notes 3.1 (Part 3) Empirical Probability, Subjective Probability and the law of large numbers.

Empirical Probability Empirical (or Statistical) Probability: –Is based on observations obtained from a probability experiment. –These problems will usually have frequency or survey. P (E) = Frequency of event E Total frequency

Example 1 A pond contains 3 types of fish, bluegills, redgills and crappies. Bluegill13 Redgill17 Crappies10 What is the probability that someone catches a bluegill fish next?

Example 1 A pond contains 3 types of fish, bluegills, redgills and crappies. Bluegill13 Redgill17 Crappies10 ∑ F = 40 What is the probability that someone catches a bluegill fish next? 13 40

Example 2 An insurance company determines that in every 100 claims, 4 are fraudulent. What is the probability that the next claim will be fraudulent? What is the probability that the next claim will not be fraudulent?

Example 2 An insurance company determines that in every 100 claims, 4 are fraudulent. What is the probability that the next claim will be fraudulent? 1 25 What is the probability that the next claim will not be fraudulent?24 25

Go to page 114 in your book to do example number 5 and try it yourself 5.

Subjective Probability Probability results from intuition, educated guesses and estimates. It does not have a formula, just based on a gut feeling.

Law of large numbers As an experiment is repeated over and over, the empirical probability of an event approaches the theoretical (actual) probability of the event. (Coin example)

Types of probabilites Classical Probability: The number of outcomes in a sample space is know and each outcome is equally likely to occur. Empirical Probability: The frequency of outcomes in the sample space is estimated from experimentation. Subjective Probability: Probabilities based from intuition, educated guesses and estimates.

Go to Page 115 to do Example 6 and the try it yourself 6. And look at blue insight box on the left hand side.

Notes 3.1 (Part 4) Complement of Event E: is the set of all outcomes in a sample space that are not included in event E. The complement event is usually denoted by P ( not event E). In this case just subtract event E from the total of events to give you the complement of event E.

Example 1 On a 10 sided die, what is the probability that you roll a 3. The complement to this would be, what is the probability that you do not roll a 3.

Example 2 Bluegills13 Redgills 17 Crappies10 ∑ F = 40 What is P( not a Bluegill) What is P( not a bluegill or a Redgill)