ou are trying out for the school play. The probability that you are chosen to in the play is 0.5 . The probability that you get a lead role is 0.1 . What is the robability that you get a lead role, given that you are chosen to be in the Alay? 0.4 B. 0.6 c. 0.3 D. 0.2

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.

3. Combinations and Probabilities: 20 pts. You are tasked with creating a code using the following three conditions: 1. The code must consist of exactly 4 characters. 2. Each character can be one of the following: A, B, C, or D. 3. The code can repeat characters, but the first character must be different from the last character. How many different codes can you create based on these condi- tions? You MUST show all of your steps to receive full credit.

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

Question 2 (1 point) Using the definition of probability, what are the chances of pulling a King out of a deck of 52 cards? \( 1 / 52 \) \( 4 / 52 \) \( 8 / 52 \) \( 2 / 52 \)