Please put in Word format.

Suppose that there are four people in the Smith family. Their favorite ice cream place is just up the street, and it never runs out of any flavor of ice cream! The family members always place their order (a single scoop ice cream cones) in order - youngest to oldest. Each person is equally likely to choose either peanut butter blast or triple chocolate fudge brownie (the two best flavors ever created). Let PB represent peanut butter blast and let TC be the triple chocolate fudge brownie. Draw a tree diagram depicting the sample space outcomes for this experiment showing all the possible orders. Most students draw this an upload or embed the picture. (Make sure you understand what sample space is before doing this).

2. Note what it means for two events to be mutually exclusive. Define the term and provide an example using the scenario in #1.

3. Note what it means for two events to be independent. Define the term and provide an example using the scenario in #1.

4. Classify each of the following random variables as discrete or continuous.

a. X = the amount of time it takes to complete this assignment

b. X = the temperature in St. Paul, MN throughout the day

c. X = the number of flowers in a bouquet

d. X = how many episodes in the next season of a popular TV show

e. X = the quantity of eggs in a bird's nest

5. List and explain the characteristics of a binomial experiment. It's the explanation that is worth the most point here. After each characteristic (and there should be at least 4), explain it.

6. Judge this scenario:

Jason is the father in the Smith family. His favorite ice cream place is just up the street. He treats himself to an ice cream cone every Friday night. He is equally likely to choose either peanut butter blast or triple chocolate fudge brownie (the two best flavors ever created). In fact, he loves both flavors so much that he flips a coin to determine which one to get in his 52 trips during a year. His wife is happy when the coin toss results in the peanut butter blast because Jason is a messy eater, and that flavor is easier to successfully wash out of the shirt.

Question: Does this scenario meet the qualifications of a binomial experiment? Why or why not? (use the four characteristics you wrote about in #5 to justify your response)