13.1 Theoretical Probability Objectives: List or describe the sample space of an experiment. Find the theoretical probability of a favorable outcome. Standard Addressed: 2.7.11 D: Use theoretical probability distributions to make judgments about the 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. The sum of the probabilities is 1.

Terminology: Definition/Example : 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 outcome rolling a 3 or rolling a 5

Ex. 1a.

Ex. 1b. Find the sample space for the experiment of tossing a coin 3 times. 1st toss 2nd toss 3rd toss H T

Ex. 2

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. 3

Ex. 4

Ex. 5a. 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. 2/9 = 22.2%

Ex. 5b. 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. 4/9 = 44.4%

Ex. 6 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. 2/15 = 13.3%

Ex. 7 Blade logs his electronic mail once during the time interval from 1 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. 10/60 = 1/6 = 16.6% b). from 1:30 p.m. to 1:35 p.m. 5/60 = 1/12 = 8.3%

a). 8:04 a.m. 1/5 = 20% b). 8:02 a.m. 3/5 = 60% c). 8:01 a.m. Ex. 8 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. 1/5 = 20% b). 8:02 a.m. 3/5 = 60% c). 8:01 a.m. 4/5 = 80% d). 8:03 a.m. 2/5 = 40%