Download Lesson 12-7

Note for Lesson 12 – 7: Theoretical and Experimental Probability
12-7.1 – Finding Theoretical Probability
Vocabulary:
Probability – How likely an event is to occur
Theoretical Probability – The ratio of the number of favorable outcomes to the total
number of possible outcomes
Experimental probability – The ratio of the number of times an event actually happens to the number of
times the experiment is done
Outcome – The result of a single trial in a probability experiment
Sample Space – The set of all possible outcomes in a situation
Event – Any group of outcomes in a situation involving probability
Complement – All possible outcomes that are not in the event
Odds – A ratio that compares the number of favorable and unfavorable outcomes
An experiment is any activity that is based on chance. In an experiment each attempt is called a trial and the
result of that trial is called an outcome. All of the possible outcomes of an experiment is called the sample
space. So if you were rolling a die, the sample space would be the numbers 1, 2, 3, 4, 5, and 6 while the
outcome would be whatever was rolled on that trial.
Examples: Identify the sample space and the outcome shown for each experiment
Tossing two coins: Sample space (HH, HT, TH, TT)
Spinning a spinner with 4 colors: Sample Space (red, blue, black, and white)
When the outcomes in a sample space have the same chance of occurring then we say the outcomes are equally
likely. The roll of a die is an example of equally likely results. However, if the die an 2 ones on it and no 6
then the outcomes would not be equally likely because the one would have a greater probability since it occurs
twice.
Theoretical probability is the probability that something should happen based on outcomes all being equally
likely.
favorable outcomes
Total outcomes
Examples: Find the theoretical probability of each event.
Theoretical probability can be found by
Rolling a 3 on a die:
1
6
3 1
or
6 2
13 1

Picking a heart from a deck of cards:
52 4
12-7.2 – Find the complement of an event.
Rolling a number greater than 3:
The complement is everything that you do not want. The sum of the probability and its complement is always
1. For example, if there is a 25% chance of drawing a spade from a deck of cards, then there is a 75% chance
you will not draw a spade from the deck.
Examples:
The weather forecaster predicts a 20% chance of rain. What is the probability it will not rain?
100 – 20 = 80
80% chance it will not rain
3
The probability of choosing a red marble is , what is the probability of not drawing a red marble?
4
1–¾=¼
¼ chance of not drawing a red marble.
12-7.3 – Finding odds
Odds are shown as a ratio of good results to bad result. The two numbers given in the odds will add up to the
total number of outcomes.
1
If the odds of spinning a 4 on a spinner is 1:3, What is the probability of spinning a 4?
Spinning anything
4
3
other than a 4?
4
Examples: The odds the choosing a green marble from a bag are 5:3. What is the probability of choosing a
5
green marble?
8
12-7.4 – Finding Experimental Probability
The experimental probability of an experiment is what actually happens. The experimental probability could
be different for the same type of experiment run different times. For example, if student A flips a coin 10 times
and student B flips a coin 10 times the experimental probability of flipping a head could be different.
Number of time an event occurs
To find the experimental probability of an event =
Number of trials
Examples: An experiment consists of spinning a spinner. The results are listed in the table. Find the
experimental probability of the following results.
Outcome Frequency
8
8
2
Red
7
 or
a) Spinner lands on blue
7  8  5 20 5
Blue
8
Green
5
78
15 3
 or
b) Spinner does not land on green
7  8  5 20 4
12-7.5 – Using Experimental Probability
We can use the experimental probability to predict what would happen in a future trial. If we find the
experimental probability we can multiply it by the number of trials we want to run to predict the results.
Example: A manufacturer inspects 800 light bulbs and finds 796 of them have no defects.
a) what is the experimental probability that a light bulb chosen has no defect?
796 199
or
or 99.5%
800 200
b) If the manufacturer inspects a shipment of 2000 light bulbs. Predict the number of light bulbs that
have no defects.
199
* 2000  1990
200