Transcript 10.1 Introduction to Probability

10.1 Introduction to
Probability
Objective: Find the theoretical probability of an
event. Apply the Fundamental Counting Principle.
Standard: 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.
I. The terminology used to discuss probabilities is given below:
Definition
Trial: a systematic opportunity for an event to occur
Experiment: 1 or more trials
Sample Space: the set of all possible outcomes
of an event
Event: an individual outcome
or
any specified combination of outcomes
Example
rolling a # cube
rolling a # cube 10 times
1, 2, 3, 4, 5, 6
rolling a 3
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.
2/9 = 22.2%
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.
4/9 = 44.4%
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.
2/15 = 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 email 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.
10/60 = 1/6 = 16.7%
b). from 1:30 p.m. to 1:35 p.m.
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.
1/5 = 20%
c). 8:01 a.m.
4/5 = 80%
b). 8:02 a.m.
3/5 = 60%
d). 8:03 a.m.
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
Academic Algebra II- Section 10.1 Level B