Homework
Geometry & Probability
Unit C
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Lesson 4 – Theoretical Probability
1. Find the theoretical probability of the event P(12) when rolling a 12-sided die. _______
2. The probability of exactly two heads when a fair coin is tossed twice is ¼.
Classify the statement as an example of theoretical probability or experimental probability.
3. A class is flipping a coin to see what the probability of getting heads is. The class flips a coin
48 times and heads comes up 35 times and tails comes up 13 times.
a) What is the experimental probability of getting heads? _____________
b) What is the theoretical probability of getting heads? ______________
4. Richard, Lenny, Hanne, and Rakel together buy one season ticket to see a basketball team.
a) If there are 52 games included, what is the expected amount of games that Richard
and Lenny will see? __________________
b) The data from a simulation of the situation is shown in the table. The values
represent the number of times each person goes to a game.
Simulation Results
Richard
Lenny
Hanne
Rakel
Total
18
8
16
10
52
How do the results from the simulation compare to the expected amount of games?
5. Reasoning The spinner is divided into eight equal parts.
a) Find the theoretical probability of landing on section(s)
P(greater than 5) of the spinner. ______________
8
7
6
1
2
3
5 4
b) Are you able to use the probability to predict future events? Explain.
6. Marbles There are 60 marbles in the bag. The bag has 23 green marbles, 28 red marbles, and
9 yellow marbles. Silas selects a marble from the bag 20 times, and of those he picks a green
marble 15 times.
a) What is the experimental probability of selecting a green marble? _________
b) What is the theoretical probability of selecting a green marble? _________
page 2
G&P Unit C Lesson 4
7. Error Analysis There are six workers at a small store. One person is chosen at random to
close the store each day. Ryan and Nadia believe that the total number of times they will close
the store over 192 days is 32 times combined.
a) How many times are Ryan and Nadia expected to close the store over 192 days combined?
Show your work.
_________________
b) Which of the following is the correct comparison?
❍ A. The result from the simulation is less than the expected result.
❍ B. The result from the simulation is greater than the expected result.
❍ C. The result from the simulation is the same as the expected result.
c) What error might Ryan and Nadia have made?
❍ A. They found the expected value for four people
❍ B. They found the expected value for one person.
❍ C. They found the expected value for five people.
❍ D. They found the expected value for three people.
8. The probability of selecting a consonant at random from the alphabet is 21/26.
a) Decide whether the situation is an example of experimental probability or theoretical
probability. ______________________
b) Describe another example that is the other type of probability.
9. A student has a one-dollar bill, a five-dollar bill, and a ten-dollar bill in a box. The student
selects a bill from the box 47 times and selects the one-dollar bill 15 times.
a) What is the experimental probability of selecting the one-dollar bill? _________
b) What is the theoretical probability of selecting the one-dollar bill? ______
10. Think About the Process There are five different colored bean bags in a box.
a) What should be the first step before using the theoretical probability formula?
❍ A. The first step is to count the number of favorable outcomes.
❍ B. The first step is to pick the event.
❍ C. The first step is to count the total number of possible outcomes.
❍ D. The first step is to check that all outcomes are equally likely to occur
b) What is the probability of pulling the yellow-colored bean bag from the box?
P(yellow bean bag) = _________________