Transcript 2.8 Probability and Odds

2.8 Probability and Odds
GOAL
1
FINDING THE PROBABILITY OF AN EVENT
VOCABULARY
•probability of an event
•outcomes
•event
•theoretical probability
•favorable outcomes
•experimental probability
EXAMPLE 1
Theoretical Probability and Experimental Probability
Although these are technically different, the way we find
each type of probability is similar.
Number of favorable outcomes
Theoretical Probability P =
Total number of outcomes
Experimental Probability P =
# of favorable outcomes observed
Total number of trials
In other words:
Probability P =
# of Favorable outcomes
# of Possible outcomes
Extra Example 1
a. You have 2 red and 2 black socks in a drawer. You reach
in and pick two without looking. What is the probability P
that they do not match?
A picture can help solve this.
Unfavorable
Determine if each outcome
is favorable or unfavorable.
Favorable
Favorable
# of Favorable outcomes
P=
# of Possible outcomes
Unfavorable
2

4
Note: We will write probabilities as
 0.5
decimal numbers.
Extra Example 1 (cont.)
b. In a group of students, 12 ride the bus to school, 8 are
driven to school, and 5 walk. One of the students is chosen
at random from the group. What is the probability P that
the student walks to school?
First, determine the number of favorable outcomes and the
number of possible outcomes.
Favorable outcomes = 5, Possible outcomes = 25
Use the equation for probability.
EXAMPLE 2
# of Favorable outcomes
P=
# of Possible outcomes
5

25
 0.2
Extra Example 2
Use the circle graph below showing the responses of 250
college students to a survey asking “Which factor is most
likely to influence your job choice after graduation?” If you
were to ask a randomly chosen college student this
question, what is the experimental probability that the
student would say “type of company”?
Influences on Job Choices
Size of
Company
17
Location
103
Type of
Company
37
Salary 93
P

Favorable
Possible
37
103  93  37  17
 0.15
Checkpoint
Last January it snowed 7 days, was sunny 18 days, and
was cloudy 6 days.
a. Based on this information, what is the probability that it
will snow on a randomly chosen day in January?
7
 0.23
31
b. Is the probability in part (a) experimental or theoretical?
Experimental
2.8 Probability and Odds
GOAL
2
FINDING THE ODDS OF AN EVENT
Although similar, finding the odds that an event will occur
is slightly different than finding the probability it will occur.
Favorable outcomes
Odds =
Unfavorable outcomes
So how are unfavorable outcomes, favorable outcomes, and
possible outcomes related?
Possible outcomes = unfavorable + favorable
This means that if we know two of these, we can find the third:
Favorable outcomes = possible - unfavorable
Unfavorable outcomes = possible - favorable
EXAMPLE 3
Extra Example 3
You randomly choose a letter from the word SUMMER.
What are the odds that the letter is a vowel?
First, determine the number of favorable and unfavorable
outcomes.
Favorable (U, E): 2
Unfavorable (S, M, M, R): 4
Then use the equation for odds.
Favorable outcomes
Odds =
Unfavorable outcomes
Note: Odds are not
written as a decimal,
but as a ratio of two
numbers using “to.”
2
=
4
= 1 to 2
How are probability and odds related?
You can think of it in two ways:
Probability event will occur
Odds =
Probability event will not occur
Probability event will occur
Odds =
1  Probability event will occur 
EXAMPLE 4
Extra Example 4
The probability that a randomly chosen 4 digit security code
contains at least one zero is 0.34. What are the odds that a
4 digit security code contains at least one zero?
Since we know the probability the code contains at least
one zero, we use the following formula and then substitute
and simplify.
Probability event will occur
Odds =
1  Probability event will occur 
0.34

1- 0.34
0.34 100


0.66 100

34
66
 17 to 33
Checkpoint
1. A candy dish contains 12 miniature chocolate bars and
21 hard candies. What are the odds that a candy picked at
random from the dish will be a hard candy?
7 to 4
2. In a shoe factory, the probability of a defective shoe
being produced is 0.005. What are the odds of producing a
defective shoe?
1 to 199
QUESTIONS?