10.1 Introduction to Probability Objective: Find the theoretical probability of an event. Apply the Fundamental Counting Principle. Standard: D Use theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations. likelihood of various outcomes in uncertain situations.

The overall likelihood, or probability, of an event can be discovered by observing the results of a large number of repetitions of the situation in which the event may occur. Outcomes are random if all possible outcomes are equally likely. I. The terminology used to discuss probabilities is given below: DefinitionExample Trial: a systematic opportunity for an event to occur rolling a # cube Experiment: 1 or more trials rolling a # cube 10 times Sample Space: the set of all possible outcomes 1, 2, 3, 4, 5, 6 of an event Event: an individual outcome rolling a 3 or any specified combination of outcomes rolling a 3 or rolling a 5

II.Theoretical Probability: is based on the assumption that all outcomes in the sample space occur randomly. If all outcomes in a sample space are equally likely, then the theoretical probability of event A, denoted P(A), is defined by: P(A) = ___number of outcomes in event A___ number of outcomes in the sample space

Ex 1. Find the probability of randomly selecting a red disk in one draw from a container that contains 2 red disks, 4 blue disks, and 3 yellow disks. Ex 2. Find the probability of randomly selecting a blue disk in one draw from a container that contains 2 red disks, 4 blue disks, and 3 yellow disks. Ex 3. Find the probability of randomly selecting an orange marble in one draw from a jar containing 8 blue marbles, 5 red marbles, and 2 orange marbles. 2/9 = 22.2% 4/9 = 44.4% 2/15 = 13.3%

* b). Find the probability of a dart landing in region B. * c). Find the probability of a dart landing in region C.

IV. Application Computers - 1). Bruce logs onto his account once during the time interval from 1p.m. to 2 p.m. Assuming that all times are equally likely, find the probability that he will log on during each time interval. a). from 1:30 p.m. to 1:40 p.m. b). from 1:30 p.m. to 1:35 p.m. 10/60 = 1/6 = 16.7%5/60 = 1/12 = 8.3%

2). A bus arrives at Jason’s house anytime from 8 to 8:05 a.m. If all times are equally likely, find the probability that Jason will catch the bus if he begins waiting at the given time. a). 8:04 a.m. b). 8:02 a.m. c). 8:01 a.m. d). 8:03 a.m. 1/5 = 20% 3/5 = 60% 4/5 = 80% 2/5 = 40%

V.Fundamental Counting Principle: If there are m ways that one event can occur and n ways that another event can occur, then there are m ● n ways that both events can occur. Tree diagrams illustrate the fundamental counting principle.

Writing Activities

Review of Introduction to Probability

Homework Integrated Algebra II- Section 10.1 Level A Honors Algebra II- Section 10.1 Level B