Rory’s Story Cubes.
Draw the probability distributions of one Story Cube and one Numbered Die.
For which of these can you calculate the mean & SD?
That one is a Random Variable!
Calculate the Mean & Standard Deviation of the random variable.
Outcome | | | | | | |
Probability | | | | | | |
How much should you charge if it is a uniform distribution?
How much should you charge if the distribution is skewed right? What does your distribution look like?
Create a distribution using all 5 of the bill values where the expected value is $__.
Two envelopes.
There are two envelopes containing cash. One envelope has twice the amount of money as the other. You get to select one and peek inside. Then you are given the opportunity to switch envelopes.
Should you
switch?
Tetrahedral Die.
A fair 4-sided die has face number 1, 2, 3, and x.
What number should be on the 4th face so the expected value is 5?
What is the standard deviation
of this random variable?
Value | 1 | 2 | 3 | x |
Probability | | | | |
Dice Difference.
Create a distribution for the difference in two dice rolls:
What are the mean and standard deviation of this distribution?
Difference | | | | | | |
Probability | | | | | | |
Probability Spinner
Create a non-trivial probability model for this spinner.
Assign probabilities so that E(spinner) = 5 pts.
Calculate the standard deviation of this
random variable.
1 pt
2 pts
20 pts
5 pts
Imagine a school assembly with 250 students. Everyone stands up and flips a coin. People with tails sit down. People with heads flip again.
Do you think anyone will get 6 heads in a row?
How many heads in a row do you expect the last one standing to have flipped?
Best of 7.
Create the model of the number of games played in a 7-game series if everyone is equally likely to win.
What if there is a 60-40 chance of winning?
Book Exchange.
Every year on January 1st a group of 4 friends do a book exchange. They put all 4 names in a hat and shake it up. Each person randomly draws a name from the hat and gives their book to that person. However, if anyone draws their own name, they all put their names back into the hat and start over.
Perform a simulation to create a distribution for the random variable, X = the number of people who select their own name. Let's create a distribution of the data for the whole class:
Calculate the mean and standard deviation of the distribution.
The Grand
Game.
If you already have $1,000, what is the expected value of going for $10,000?
Coin
Flip.
Someone offers you a bet on a fair coin:
Heads wins $200, tails loses $100.
Would you take the bet?
What is the mean & standard deviation of this bet?
Would you rather make this bet once or 20 times?
What is the mean & standard deviation of these 20 bets?
What is the probability that you make money?
X + X vs. 2X.
Draw the distribution for rolling a fair 4-sided die? Find E(X) and SD(X).
Draw the distribution for doubling the value of each face (2X)? Find E(2X) and SD(2X).
Draw the distribution for the sum of two fair 4-sided dice (X + X)? Find E(X + X) and SD(X + X).
Compare the results from the three distributions.
Compare means and SDs of X+X vs 2X?
Linear Transform vs. Combining RVs
Decide whether the following scenarios are LT or Combine RV:
Capybara.
A study finds that the average capybara weighs approximately 113 pounds with a standard deviation of 18 pounds. It is later realized that the scale had a consistent error adding 3 pounds to each capybaras weight. We would also like to have the weight in kilograms (2.2lbs per 1 kg). What is the appropriate distribution in kg?
What is the average difference between the weight of two capybaras?
What is the standard deviation of those differences?
Drag Racing.
Mr. Krans & Mr. Parato enjoy drag racing. Mr. Krans’ quarter mile times are Normally distributed with a mean of 10.84 seconds and a standard deviation of 0.31 seconds. Mr. Parato’s quarter mile times are Normally distributed with a mean of 10.38 seconds and a standard deviation of 0.42 seconds.
What is the probability that Mr. Krans would beat Mr. Parato in a drag race?
Eggs.
Wordle.
What is the Mean & SD of Mr. Krans’ Wordle guesses when he finds the answer?
Marrakech.
You are Orange.
If you land on an opponent color, you pay $1 for each square of connected carpet.
You can turn left, right, or stay straight.
The dice tells you how many steps to take: 1,2,2,3,3,4.
If you hit a wall, then follow the grey path.
Which way should you go?
Rory’s Story Cubes.
Draw the probability distribution of one cube. Can you calculate the mean & SD?
Does this describe a random variable?
Draw the probability distribution for a numbered 6-sided die. Why is this a random variable?
What is the average dice roll for a fair die (aka Expected Value)?
What is the average distance a roll is from the mean?