11-3 Theoretical Probability
Warm Up
Problem of the Day
Lesson Presentation
Course 1
11-3
Theoretical Probability
Warm Up
Tim took one marble from a bag, recorded the
color, and returned it to the bag. He repeated
this several times and recorded the results.
1. Find the experimental probability that a marble
3
selected from the bag will be green. __
5
2. Find the experimental probability that a marble
4
selected from the bag will not be yellow. __
5
Course 1
11-3
Theoretical Probability
Problem of the Day
What is the probability that the sum of
four consecutive whole numbers is
divisible by 4?.
0
Course 1
11-3
Theoretical Probability
Learn to find the theoretical probability of
an event.
Course 1
11-3
Insert Lesson
Title Here
Theoretical
Probability
Vocabulary
theoretical probability
equally likely
fair
Course 1
11-3
Theoretical Probability
Another way to estimate probability of an event
is to use theoretical probability. One situation
in which you can use theoretical probability is
when all outcomes have the same chance of
occurring. In other words, the outcomes are
equally likely.
Course 1
11-3
Theoretical Probability
An experiment with equally likely outcomes is
said to be fair. You can usually assume that
experiments involving items such as coins and
number cubes are fair.
Course 1
11-3
Theoretical Probability
Additional Example 1A: Finding Theoretical
Probability
A. What is the probability that this fair spinner
will land on 3?
There are three possible outcomes
when spinning this spinner: 1, 2,
or 3. All are equally likely because
the spinner is fair.
P(3)= _________________
3 possible outcomes
There is only one way for the spinner to land on 3.
1
way event can occur
1
__________________
__
P(3)= 3 possible outcomes =
3
Course 1
11-3
Theoretical Probability
Additional Example 1B: Finding Theoretical
Probability
B. What is the probability of rolling a number
greater than 4 on a fair number cube?
There are six possible outcomes when a fair
number cube is rolled: 1, 2, 3, 4, 5, or 6. All
are equally likely. There are 2 ways to roll a
number greater than 4:5 or 6.
P(greater than 4)= _________________
6 possible outcomes
2 ways events can occur __
2
____________________
P(greater than 4)=
6 possible outcomes = 6
Course 1
11-3
Theoretical Probability
Try This: Example 1A
A. What is the probability that this fair
spinner will land on 1?
There are three possible outcomes
when spinning this spinner: 1, 2,
or 3. All are equally likely because
the spinner is fair.
P(3)= _________________
3 possible outcomes
There is only one way for the spinner to
land on 1.
1
way event can occur
1
__________________
__
P(3)= 3 possible outcomes =
3
Course 1
11-3
Theoretical Probability
Try This: Example 1B
B. What is the probability of rolling a number
less than 4 on a fair number cube?
There are six possible outcomes when a fair
number cube is rolled: 1, 2, 3, 4, 5, or 6. All
are equally likely. There are 3 ways to roll a
number greater than 4:3, 2 or 1.
P(less than 4)= _________________
6 possible outcomes
3 ways events can occur
1
__
____________________
=
P(less than 4)=
6 possible outcomes
2
Course 1
11-3
Theoretical Probability
Think about a single experiment, such as tossing
a coin. There are two possible outcomes, heads
or tails. What is P(heads) + P(tails)?
Experimental Probability
(coin tossed 10 times)
H
llll l
Course 1
Theoretical
Probability
T
llll
4
6
1
1
__
__
__
P(heads) =
P(tails) =
__
10 P(heads) = 2 P(tails)=
10
2
6
4
1
1
2
10
__
__
__
__
__
__
+
=
=1
=
=1
+
10
10 10
2
2
2
11-3
Theoretical Probability
No matter how you determine the probabilities,
their sum is 1.
This is true for any experiment—the probabilities
of the individual outcomes add to 1 (or 100%, if
the probabilities are given as percents.)
Course 1
11-3
Theoretical Probability
Additional Example 2: Finding Probabilities of
Events not Happening
Suppose there is a 45% chance of snow
tomorrow. What is the probability that it will
not snow?
In this situation there are two possible
outcomes, either it will snow or it will not
snow.
P(snow) + P(not snow) = 100%
45% + P(not snow) = 100%
-45%
-45%
_____
_____
P(not snow) = 55%
Course 1
Subtract 45%
from each side.
11-3 Theoretical Probability
Try This: Example 2
Suppose there is a 35% chance of rain
tomorrow. What is the probability that it will
not rain?
In this situation there are two possible
outcomes, either it will rain or it will not rain.
P(rain) + P(not rain) = 100%
35% + P(not rain) = 100%
-35%
_____
-35%
_____
P(not rain) = 65%
Course 1
Subtract 35%
from each side.
11-3
Theoretical
Insert Lesson
Probability
Title Here
Lesson Quiz
Use the spinner shown for problems 1-3.
2
__
1. P(2)
7
4
__
2. P(odd number)
7
4
3. P(factor of 6) __
7
4. Suppose there is a 2% chance of spinning the
winning number at a carnival game. What is the
probability of not winning? 98%
Course 1