Name: ______Block: ______Date: ______

7.1 Theoretical and Experimental Probabilities

Discovery #1:
Flip your coin to fill in the 2 “tally” columns in this table! Have Fun! / HEADS / TAILS
Trial # / # of Flips / Tally # Heads / Experimental Probability of Heads / Tally # Tails / Experimental Probability of Tails
1 / 2
2 / 10
3 / 20
4
Combine Class Data from Trial 3

Time to Analyze!!

Why are the probabilities different for each trial? Which do you think is most accurate? Why?

______Probability is what ACTUALLY occurs:

P(event)= # of favorable outcomes that occur during trial# of trials performed

What do you think the probabilities should be for getting a heads or tails when flipping a coin??

______ Probability is what SHOULD occur:

P(event) = # of favorable outcomes# of possible outcomes

Which trial is closest to the theoretical probability? Why do you think this is so?

Situation #2:

The graph shows the result of an experiment in which two number cubes were rolled.

According to the experimental probability, is the sum of 12
likely to occur?

Only ____ out of ____ sums = 12.

P(12) =

According to the experiment, which sum is most
likely to occur? ______

What is the theoretical probability to get the sum of 12?

P(12) = ______= ____

What is the theoretical probability to get a sum of 7?

P(7) = ______= ____

How does this theoretical compare to the results found in the experiment?

Situation #3: The table shows the results of spinning the equally divided 8 section spinner.

Compare the theoretical and experimental probabilities of the spinner landing on 6.

Theoretical: P = ______Experimental: P = ______

Compare: ______

Based on experimental probability, how many times would you expect the spinner

to land on 3 if the spinner is spun 200 times?

Hint--Use a Proportion:

Name: ______Block: ____ Date: ______

WKS 7.1—Experimental and Theoretical Probability Practice

1. In a survey, 120 out of 200 students said their favorite food was pizza. What is the experimental probability that a student chose pizza as his or her favorite food?

Result / # of times
1 / 6
2 / 10
3 / 8
4 / 7
5 / 10
6 / 9

Use the table that shows the results of rolling a number cube 50 times.

2.
a) Based on the results, what is the probability of getting a five? ______

b) Based on the results, how many fives would you expect to occur in 300 rolls?

c) What is the theoretical probability of getting a five? ______

d) Based on the theoretical probability, how many fives would you expect to occur in 300 rolls?

e) Compare the theoretical probability to the experimental probability. ______

3. Use the results of a survey of 200 people shown at the right. The survey determined the person’s first pet.

First pet / Number
bird / 32
cat / 56
dog / 66
rabbit / 19
other / 27

a) What is the probability that a person says his or her first pet was a cat?

b) Out of 500 people, how many would you expect to say a cat was his or her first pet?

c) What is the probability that a person says his or her first pet was a bird?

d) Out of 500 people, how many would you expect to say a bird was their first pet?

4. At figure skating practice, Michelle successfully landed 15 out of 18 attempts at a double axel. What is the experimental probability that she will successfully land a double axel?

Color / Result
Red / 12
Blue / 9
Green / 17
Yellow / 22

5. The table displays the results of spinning the spinner 60 times.

a. Based on the results, what is the probability of spinning a yellow?

b. Based on the results, how many times would you expect to spin yellow in 300 spins?

c. Did you use theoretical or experimental probability in questions a and b?

d. What is the theoretical probability of spinning yellow? ______

e. Based on the theoretical probability, how many times would you expect to spin yellow in 300 spins?

Result / No. of times
Win 1 / 24
Win 2 / 11
Win 3 / 5

6. Roseanna recorded the results in the table shown using a spinner with 8 equal-sized sections. Each section is labeled with either “Win 1” or “Win 2” or “Win 3”. How many of the sections do you predict are labeled “Win 1”?

A ) 1 B) 3 C) 5 D) 7

7. What is the theoretical probability of picking a red card out of a standard deck of cards?
(Hint: there are 52 total cards in a standard deck of cards)

8. What is the theoretical probability that you will randomly choose a day of the week that starts with “T”?

9. What is the theoretical probability that you will choose a “KING” card from a standard deck of cards?
(Hint: there are four Kings in a deck)