8A Coreq

In the next preview assignment and in the next class, you will need to think critically about the number of “successes” that would occur if a chance experiment were repeated multiple times.

How Many “Successes” Do We Expect?

At a college baseball stadium, every game features a race between three mascots: one dressed as a peanut, one dressed as a hot dog, and one dressed as a cup of soda. The winner of the race determines what discount will be available at the concession stand for the rest of the game: $1 bags of peanuts, $1 hot dogs, or $1 soft drinks. For now, let’s assume that all three mascots are equally likely to win the race, and each race is independent.

Question 1

Fill in the following table with the probability of each mascot winning the race.

Outcome	Probability
Peanut
Hot Dog
Soda

Let’s say you plan to attend two games. Let’s list all possible outcomes for the two races. “Peanut – Peanut” means the peanut wins in both the first race and the second race, “Peanut – Hot Dog” means the peanut wins in the first race and the hot dog wins in the second race, and so on.

Peanut – Peanut	Hot Dog – Peanut	Soda – Peanut
Peanut – Hot Dog	Hot Dog – Hot Dog	Soda – Hot Dog
Peanut – Soda	Hot Dog – Soda	Soda – Soda

Question 2

Maybe your favorite snack to eat during a baseball game is peanuts.

For each of the nine outcomes, record the number of times the peanut wins by writing the number in the previous table.
Assuming all three mascots are equally likely to win in each race, what is the probability that the peanut will win 0 times out of the two baseball games you attend? Write your answer as a fraction.
Assuming all three mascots are equally likely to win in each race, what is the probability that the peanut will win 1 time out of the two baseball games you attend? Write your answer as a fraction.
Assuming all three mascots are equally likely to win in each race, what is the probability that the peanut will win 2 times out of the two baseball games you attend? Write your answer as a fraction.
Fill in the following table to show the probability of each number of peanut wins.

Number of Wins

(Peanut)
Probability
Compare the table in Question 1 to the table in Question 2, Part E. How are they different?

The previous probability calculations were based on a list of all possible outcomes. This is a reasonable approach for two races because the list of outcomes is fairly short, but it wouldn’t work well for a larger set of races. For 10 races, there would be over 50,000 possible outcomes!

Another approach would be to estimate the probabilities empirically using a simulation. Since we’re assuming all three mascots are equally likely to win in each race, a statistics class decides to carry out the simulation by rolling dice: 1 and 2 represent Peanut, 3 and 4 represent Hot Dog, and 5 and 6 represent Soda.

How many times would you expect to get discounted peanuts if you attended 10 games? The following plot shows one possible set of 10 races, based on a student’s simulation using dice.

Question 3

What does each dot in the plot represent?

The winner of one race
The number of times the peanut won in a set of 10 races

Question 4

In this simulated set of 10 races, how many times did the peanut win?

Question 5

If another student used the same approach to simulate 10 races using dice, would they get the same results?

Suppose there are 24 students in a statistics class. Each student simulated a set of 10 races by rolling a fair die 10 times and recording how many times the peanut won.

Question 6