1. Lesson 10.3 – Experimental and Theoretical Probability
How can you use relative frequencies to find probabilities?

2. Vocabulary Relative frequency Experimental probability
Theoretical probability

3. When you conduct an experiment..
The relative frequency of an event is the fraction or percent of the time that the event occurs.
Relative frequency = __number of times the event occurs_____
total number of times you conduct the experiment

4. Theoretical vs. Experimental
Theoretical probability: What “should” happen when you do the experiment.
Experimental probability: What “did” happen when you conducted the experiment.
Experimental probability is sometimes called relative frequency of an event.

5. Outcome Frequency 3 red 2 3 blue 4 1 red, 2 blue 1 blue, 2 red
You have three sticks. Each stick has one red side and one blue side. You throw the sticks 10 times and record the results. Use the table to find the relative frequency of the event.
Outcome
Frequency
3 red 2
3 blue 4
1 red, 2 blue
1 blue, 2 red
Tossing 3 red
2. Tossing 1 red, 2 blue %
3. Tossing 1 blue, 2 red
4. Not tossing all red

6. Example 1:

7. What is the experimental probability of rolling an even number?
Example 1 contd:
What is the experimental probability of rolling an even number?
, 0.42, 42%

8. Example 2:

9. Theoretical probability
When all possible outcomes are equally-likely; the theoretical probability of an event is the ratio of the number of favorable outcomes to the number of possible outcomes.
P(event) = number of favorable outcomes
number of possible outcomes

10. Example 3:

11. What is the theoretical probability of choosing an X?
Example 3 contd:
or about 14.3%

12. Example 4:

13. The prize wheel was spun 540 times at a baseball game
The prize wheel was spun 540 times at a baseball game. About how many bobbleheads would you expect were won?
Example 4 contd:
90 bobbleheads

14. On Your Own
The theoretical probability of spinning an odd number on a spinner is 0.6. The spinner has 10 sections. How many sections have odd numbers?
6 sections

15. Example 5:

16. How can you tell which is experimental and which is theoretical probability?
You tossed a coin 10 times and recorded a head 3 times, a tail 7 times
P(head)= 3/10
P(tail) = 7/10
Theoretical:
Toss a coin and getting a head or a tail is 1/2.
P(head) = 1/2
P(tail) = 1/2

17. Experimental probability
Experimental probability is found by repeating an experiment and observing the outcomes.
P(head)= 3/10
A head shows up 3 times out of 10 trials,
P(tail) = 7/10
A tail shows up 7 times out of 10 trials

18. Theoretical probability
P(head) = 1/2
P(tail) = 1/2
Since there are only two outcomes, you have 50/50 chance to get a head or a tail.
HEADS
TAILS

19. Identifying the Type of Probability
A bag contains three red marbles and three blue marbles.
P(red) = 3/6 =1/2
Theoretical
(The result is based on the possible outcomes)

20. Identifying the Type of Probability
You draw a marble out of the bag, record the color, and replace the marble. After 6 draws, you record 2 red marbles
P(red)= 2/6 = 1/3
Experimental
(The result is found by repeating an experiment.)

21. pp. 417 – 418
1 – 5, 14 – 34 even