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10-6 Theoretical Probability
Warm Up
An experiment consists of spinning a
spinner 8 times. The spinner lands on
red 4 times, yellow 3 times, and green
once. Find the experimental probability
of each event.
1. The spinner lands on red.
2. The spinner does not land on green.
3. The spinner lands on yellow.
Holt Algebra 1
10-6 Theoretical Probability
When the outcomes in the sample space of an
experiment have the same chance of occurring,
the outcomes are said to be equally likely.
Holt Algebra 1
10-6 Theoretical Probability
The theoretical probability of an event is the
ratio of the number of ways the event can occur
to the total number of equally likely outcomes.
Holt Algebra 1
10-6 Theoretical Probability
Example 1A:
An experiment consists of rolling a number
cube. Find the theoretical probability of each
outcome.
rolling a 5
There is one 5
on a number
cube.
Holt Algebra 1
10-6 Theoretical Probability
Example 1B:
An experiment consists of rolling a number
cube. Find the theoretical probability of each
outcome.
rolling an odd number
There 3 odd
numbers on
a cube.
= 0.5 = 50%
Holt Algebra 1
10-6 Theoretical Probability
Example 1C:
An experiment consists of rolling a number
cube. Find the theoretical probability of each
outcome.
rolling a number less than 3
There are 2
numbers
less three.
Holt Algebra 1
10-6 Theoretical Probability
Example 2: Try It Now
An experiment consists of rolling a number cube.
Find the theoretical probability of each outcome.
a. Rolling an even number
There 3 even
numbers on
a cube.
= 0.5 = 50%
b. Rolling a multiple of 3
There are 2
multiples
of three.
Holt Algebra 1
10-6 Theoretical Probability
Reading Math
The probability of an event can be written as
P(event). P(heads) means “the probability that
heads will be the outcome.”
Holt Algebra 1
10-6 Theoretical Probability
When you toss a coin, there are two possible
outcomes, heads or tails. The table below shows
the theoretical probabilities and experimental
results of tossing a coin 10 times.
Holt Algebra 1
10-6 Theoretical Probability
The sum of the probability of heads and the
probability of tails is 1, or 100%. This is because it is
certain that one of the two outcomes will always
occur.
P(event happening) + P(event not happening) = 1
Holt Algebra 1
10-6 Theoretical Probability
The complement of an event is all the outcomes
in the sample space that are not included in the
event. The sum of the probabilities of an event and
its complement is 1, or 100%, because the event
will either happen or not happen.
P(event) + P(complement of event) = 1
Holt Algebra 1
10-6 Theoretical Probability
Example 3:
A box contains only red, black, and white blocks.
The probability of choosing a red block is , the
probability of choosing a black block is . What is
the probability of choosing a white block?
P(red) + P(black) + P(white) = 100% Either it will be a
white block or
25% + 50% + P(white) = 100%
not.
75% + P(white) = 100%
–75%
–75% Subtract 75%
from both
P(white) = 25%
sides.
Holt Algebra 1
10-6 Theoretical Probability
Example 4: Try It Now
A jar has green, blue, purple, and white
marbles. The probability of choosing a green
marble is 0.2, the probability of choosing blue
is 0.3, the probability of choosing purple is 0.1.
What is the probability of choosing white?
Either it will be a white marble or not.
P(green) + P(blue) + P(purple) + P(white) = 1.0
0.2 + 0.3 + 0.1 + P(white) = 1.0
0.6 + P(white) = 1.0
– 0.6
– 0.6
P(white) = 0.4
Holt Algebra 1
Subtract 0.6 from
both sides.
10-6 Theoretical Probability
Odds are another way to express the likelihood
of an event. The odds in favor of an event
describe the likelihood that the event will occur.
The odds against an event describe the likelihood
that the event will not occur.
Odds are usually written with a colon in the form
a:b, but can also be written as a to b or .
Holt Algebra 1
10-6 Theoretical Probability
Holt Algebra 1
10-6 Theoretical Probability
The two numbers given as the odds will add up to
the total number of possible outcomes. You can use
this relationship to convert between odds and
probabilities.
Holt Algebra 1
10-6 Theoretical Probability
Reading Math
You may see an outcome called “favorable.” This
does not mean that the outcome is good or bad.
A favorable outcome is the outcome you are
looking for in a probability experiment.
Holt Algebra 1
10-6 Theoretical Probability
Example 5A:
The probability of rolling a 2 on a number
cube is
. What are the odds of rolling a 2 ?
The probability of rolling a 2 is . There are 5 unfavorable
outcomes and 1 favorable outcome, thus the odds are 1:5.
Odds in favor are 1:5.
Holt Algebra 1
10-6 Theoretical Probability
Example 3B:
The odds in favor of winning a contest are
1:9. What is the probability of winning the
contest?
The odds in favor of winning are 1:9, so the odds against are
9:1. This means there is 1 favorable outcome and 9
unfavorable outcomes for a total of 10 possible outcomes.
The probability of winning the contest is
Holt Algebra 1
10-6 Theoretical Probability
Example 5C:
The odds against a spinner landing on red are
2:3. What is the probability of the spinner
landing on red?
The odds against landing on red are 2:3, so the odds in
favor are 3:2. This means there are 3 favorable outcomes
and 2 unfavorable outcomes for a total of 5 possible
outcomes.
The probability of landing on red is
Holt Algebra 1
10-6 Theoretical Probability
Example 6: Try It Now
The odds in favor of winning a free drink are
1:24. What is the probability of winning a
free drink?
The odds in favor of winning are 1:24, so the odds
against are 24:1. This means there is 1 favorable
outcome and 24 unfavorable outcomes for a total of 25
possible outcomes.
The probability of winning the free drink is
Holt Algebra 1