Download Chapter 7 Assignment

Chapter 7 Assignment
These assignments will NOT be accepted unless typed. (Yes, the tables must be
typed too. You are to make tables, not columns. If you need help with creating
tables, just ask.) You will not be turning in a preliminary draft. You can still ask
me questions to make sure you are doing it correctly. Type the experiment
questions along with the results. You will be marked down without these.
You will perform three probability experiments:
1) Rolling dice (one and two)
2) Selecting a number 1-10 from a bag (with replacement) and using randint
function to generate a numbers 1-10 list (uses “with replacement”)
3) Another probability experiment of your choice involving the procedure of
“without replacement”
Chapter 7 Schedule
Date
Topic/Assignment
Date
Topic/Assignment
3/21-3/22
PPT: Chance & Probability
3/30
PPT: Permutations,
Combinations, Fundamental
Counting Principle
GW: Shut the Box
3/23
PPT: Probability Models, Rules
4/2
GW: Jeopardy
4/3
Take any missing exams
4/4-4/5
Turn in Chapter 7 HW
of Probability
HW: Intro to Ch. 7 Probability
Experiments Assignment
3/26
PPT: Addition Rule
GW: White Book Activity
3/27
3/28-3/29
PPT: Multiplication Rule,
Conditional Probability
Take Chapter 7 Test
GW: White Book Activity
HW: Hand out ec assignment
Numb3rs Episode 303
GW: Birthday Surprise
(Complements)
Report on the following results for experiment #1
1) What is the sample space for rolling 1 die?
2) What are the theoretical probabilities for the outcomes in rolling 1 die, in
fraction form? Write a probability model for this.
3) Roll 1 die 36 times. Record your results. How does your empirical data
compare with the theoretical probability for the outcomes? Record the
probabilities (empirical and theoretical) for the sample space, side by side in a
table in fraction form.
4) Are the outcomes for this experiment mutually exclusive and independent?
Explain your answer.
5) What is the sample space for rolling 2 dice? (Use the sum of the dice)
6) What are the theoretical probabilities for the outcomes in rolling 2 dice, in
fraction form? Write a probability model for this.
7) Roll 2 dice 36 times. Record your results (their sums). How does your
empirical data compare with the theoretical probability for the outcomes?
Record the probabilities (empirical and theoretical) for the sample space, side
by side in a table in fraction form.
8) Are the outcomes for this experiment mutually exclusive and independent?
Explain your answer.
9) If your empirical probabilities did not match the theoretical probabilities, how
can you do the experiment differently so they could match, or come closer, the
next time?
10)
Using the empirical and theoretical data you have gathered for rolling 1 die
and 2 dice, create the following:
a. An event using the theoretical data for rolling 2 dice (i.e., rolling an odd
number—use something different please!).
i. Calculate the theoretical data and empirical data based on this
new event.
ii. Make comparisons regarding how close your data is now to how
close it was originally.
b. Using the same event as part a above for rolling 2 dice, repeat using
theoretical data for rolling 1 die (i.e., rolling an odd number – again,
please don’t use that one).
i. Calculate the theoretical data and empirical data based on this
event.
ii. Make comparisons regarding how close your data is now to how it
is to the data in part a. In some cases, it may be that part b was
not possible because you chose something part a was able to do
that part b wasn’t. Don’t change your events.
Report on the following results for experiment #2
1) What is the sample space?
2) What are the theoretical probabilities for each outcome? Write out as a
probability model.
3) Find the theoretical probability of choosing a 5 or an 8.
4) Choose 50 numbers using randint(1,10,50). List the numbers which were
drawn, in order.
5) What was the empirical probability of choosing a 5 or an 8 in your probability
experiment?
6) Find the theoretical probability of choosing a number less than 4 or an odd
number. Write the formula for this.
7) Choose 50 numbers by choosing numbers from a bag (choose the number,
record it, replace it, then repeat).
8) What was the empirical probability of choosing a number less than 4 or an odd
number in your probability experiment?
9) Are the outcomes for either part of this experiment mutually exclusive and
independent? Explain your answer.
10)
Did changing the method of choosing numbers have an effect on the
outcomes? Explain.
Report on the following results for experiment #3
1) What is your probability experiment?
2) What is your sample space?
3) What are the theoretical probabilities for each outcome?
4) Conduct your probability experiment. Your experiment must include a
procedure “without replacement”; that is if you choose a number from a bag,
you don’t put it back. The probability of the next item chosen has changed
(out of 10 has now changed to out of 9). You need to repeat the experiment a
sufficient number of times as to get enough data as you did in experiments #1
and 2.
5) Report your data. What are the empirical probabilities for this data?
Compare this data to the theoretical probabilities. Were they close?
6) If your experiment was “mutually exclusive”, how can you change it to “not
mutually exclusive”; if it was “not mutually exclusive”, how can you change it
to “mutually exclusive”?