What does it mean for two events to be independent in probability?

Question 4 (1 point) In order for 2 events to be mutually exclusive, they occur at the same time. True False

Question 1 (1 point) Choose 3 ways a sample space can be represented. (you will select 3 of these) Select 3 correct answer(s) List Taragraph Tree Diagram Equation

The Fundamental Counting Principle (FCP) store enlls three types of shirts: red, blue, and green. Each shirt is available three different sizes: small, medium, and large. a.) Draw a tree diagram that represents all the possible combinations of Use the tree diagram to calculate the total number of different shirt com- tions (color and size) available in the store (5 pts). Suppose a customer randomly selects one shirt from the store. What is robability that the selected shirt is cither blue or large in size? (5pts) What is the probability of a customer purchasing a shirt that is large irple? (5pts)

There are 10 people at a meeting and there are 3 different door prizes to give out. How many ways can we select 3 people to receive the door prizes?

4 Permutations and Probabilities: 20 pts, Part A: 10 pts. You are tasked with organizing a group of 6 people: Allice, Bob, Charlie, David, Eva, and Frank. How many different ways can you arrange these 6 people in a line? Show your work to receive full credit. Part B: 10 pts. If the arrangement from Part A must have Alice and Bob standing next to each other, what is the probability that Alice and Bob will be next to each other in a random arrangement? Show your work to receive full credit.