Presentation on theme: "13.1 Theoretical Probability"— Presentation transcript:
1 13.1 Theoretical Probability Objectives: List or describe the sample space of an experiment. Find the theoretical probability of a favorable outcome. Standard Addressed: D: Use theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations.
2 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.
3 Terminology: Definition/Example : Trial: a systematic opportunity for an event to occurrolling a # cubeExperiment: 1 or more trials rolling a # cube 10 timesSample Space: the set of all possible outcomes 1, 2, 3, 4, 5, 6 of an eventEvent: an individual outcomerolling a 3 or any specified combination ofoutcome rolling a 3 or rolling a 5
7 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 thetheoretical 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
10 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%
11 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%
12 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%
13 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%
14 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%