We will be working with Bernoulli trials to model probability. A Bernoulli trial has only two outcomes (success or failure) and the probability of that success is the same for each trial.We can model the probability of an event by doing repeated trials and recording the proportion of successes for the desired outcome.

Mario Party is a party video game featuring characters from the Mario franchise. The game features a board where players roll a dice to move forward along a path. For each round a player can choose to roll a normal 6-sided die {1,2,3,4,5,6} or their character's special die. The special dice are unique to each character, for example, Mario's is {1,3,3,3,5,6}.

Attached Below is a spreadsheet of each character and their corresponding dice. Note values with + or - in front indicate the player will either gain or lose coins. Change these values to a zero for any calculations you do.

Character	Side 1	Side 2	Side 3	Side 4	Side 5	Side 6
Boo	-2	-2	5	5	7	7
Bowser	-3	-3	1	8	9	10
Bowser Jr.	1	1	1	4	4	9
Daisy	3	3	3	3	4	4
Diddy Kong	0	0	0	7	7	7
Donkey Kong	+5	0	0	0	10	10
Dry Bones	1	1	1	6	6	6
Goomba	+2	+2	3	4	5	6
Hammer Bro	+3	1	1	5	5	5
Koopa	1	1	2	3	3	10
Luigi	1	1	1	5	6	7
Mario	1	3	3	3	5	6
Monty Mole	+1	2	3	4	5	6
Peach	0	2	4	4	4	6
Pom Pom	0	3	3	3	3	8
Rosalina	+2	+2	2	3	4	8
Shy Guy	0	4	4	4	4	4
Waluigi	-3	1	3	5	5	7
Wario	6	6	6	6	-2	-2
Yoshi	0	1	3	3	5	7
D6 (normal dice)	1	2	3	4	5	6

Q1. How far, on average, should I expect to move on the board by using each specialty die? -(use a probability principle to figure this out). Describe which principle you are using and how it applies.

Label each character based on whether it is better to use their specialty die or the regular die (D6).

Q2. Pick one of the character's specialty dice and simulate 1000 rolls. Do the same for a regular die (D6).

Make an appropriate graphical summary to display both distributions.

Compare the values you calculated in question 1 with the distribution you modeled with your simulation. Does it look the way your expected? Were you surprised? Was your calculation accurate? If not, why not?

The culinary herb cilantro is very polarizing: Some people love it, but others hate it. A large survey of American adults of European ancestry found that 26% disliked the taste of cilantro.Suppose that this holds exactly true for all American adults of European ancestry. Choosing such an individual at random then has probability 0.26 of getting one who dislikes cilantro.

Use technology to simulate choosing many people at random.

Q3. Simulate drawing 25 people, then 100 people, then 400 people. What proportion, in each simulated sample, dislike cilantro? We expect (but because of chance variation we can't be sure) that the proportion will be closer to 0.26 in larger samples. Does this hold true in your samples?

Hint: the sampling applet or a Bernoulli Distribution can be used for this.

Q4. Simulate drawing a sample of 25 people 10 times (click "Reset" after each simulation) and record the percents in each simulated sample who dislike cilantro. Then simulate drawing a sample of 400 people 10 times and again record the 10 percents.

Provide an appropriate graphical summary of your results.

Which set of 10 results is less variable (the set of samples of 25 or the set of samples of 400)? Be sure to explain how you are measuring variability and describe how sample size is related to variability.