1. III. Probability B. Discrete Probability Distributions

2. Example
The discrete random variable of interest X is the number of times a 6 is rolled when rolling a die three times.
Create a tree diagram for the possible outcomes letting
A = {roll is a six} and B = {roll is not a six}.
Calculate the probability for each of the outcomes in the tree diagram.
Create the probability distribution for X (the number of times we get a 6 when we roll the die three times).
Verify that this is a valid discrete probability distribution.
Calculate the mean (expected value) for X.
Calculate the standard deviation for X.

3. Example
A roulette wheel has 38 slots, of which 18 are black, 18 are red, and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. A bet of $1 on red will win $2 if the ball lands in a red slot.
Give the discrete probability distribution for the winnings of a $1 bet on red.
Find the expected winnings (mean) for a $1 bet on red.

4. Example
Gamblers bet on roulette by placing chips on a table that lays out the numbers and colors of the 38 slots in the roulette wheel. The red and black slots are arranged on the table in three columns of 12 slots each. A $1 column bet wins $3 if the ball lands in one of the 12 slots in that column.
Give the discrete probability distribution for the winnings of a $1 column bet.
Find the expected winnings (mean) for a $1 column bet.