4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
probability
between 0 and l, inclusive
can't
happen
must
happen
* can't be negative
* can't be greater than 1
ex.
find the probability of each
1.
getting an even # on a spinner with #'s one to eight
2.
drawing a red card from a standard deck of cards
4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
probability
AND
at the same time
OR
events can occur
inclusive ­ at the same time
exclusive ­ events cannot occur
at the same time
examples Tx. page 196 # 12
If a die is rolled one time, find each probability.
a. a 2
b. a number greater than 6
c. an odd number
d. a 4 or an odd number
e. a number greater than or equal to 3
f. a number greater than 2 and an even number
4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
RULES
1.
fraction or decimal
SUMMARY
event cannot occur
2.
empty sample space
3.
4.
event certain
sum of probabilities of all outcome in
sample space is 1
**
closer probability gets to zero
more unlikely
**
closer probability gets to one
more likely
4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
complement
of an event
notation
examples
set of outcomes in the sample space NOT
included in the outcomes of the event
read as "E bar"
What would be the complement of each event?
a.
drawing a red card from a standard deck of cards
b.
spinning a spinner numbered 1 through 8 and
getting a number greater than 6
4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
N
O
T
E
S
an event and its complement make up the entire
sample space
the SUM of probability of an event and the probability
of its complement equals 1
if the probability of an event or its complement
are known, the other may be found by
subtracting the known probability from 1
4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
RULES
4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
examples
a.
b.
What is the complement of event in a?
c.
What is the probability of the complement?
d.
e.
Find the probability of drawing an ace or a king
from a standard deck of cards.
Find the sum of the event and its complement.
What does the event and its complement represent?
4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
Venn Diagram
of
Probabilities
4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
Empirical
Probability
(experimental probability ­ based on OBSERVATION)
relies on actual experience to determine probability
conduct trials
(may be given)
observe/collect frequencies
use frequency to determine probability of outcome
4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
example
100 students who enjoy fast food were asked to
name their favorite fast food restaurant. The
results are categorized in the frequency
distribution below.
Restaurant Frequency
Burger King
23
McDonalds
29
Wendy's
12
Hardees
8
Chic­fli­A
28
What is the probability of selecting a student who
whose favorite fast food restaurant is Chick­fil­A?
4­1 determine sample space and find probability 1AB.notebook
November 20, 2013
OBJECTIVE: Determine sample spaces and find the probability of
an event using classical probability or empirical
probability.
formula
for
Empirical
Probability
⇒
examples
b.
a.
W
w
N
What
who w
either