Part A 1. The handedness of a group of 3 people are Ambidextrous (A), Lefthanded (L), or Righthanded (R). Suppose two people are randomly selected with replacement (that is, a person is selected, their handedness is observed and they are returned to the group of three people). Let A be the event of selecting an ambidextrous person, L be the event of selecting a lefthanded person, and R be the event of selecting a righthanded person. (a) List all possible outcomes. (2 marks) (b) List all possible outcomes for each of the following events and find the corresponding probabilities. (8 marks) i. ii. E1 = {Exactly 1 person of type L is drawn} E2 = {The second person is right handed} iii. E3 = {At MOST one person is ambidextrous} iv. E4 = {Both people have the same handedness} (c) List all possible outcomes and find the probabilities of the following events. (12 marks: 2 for each) i. Not E3 ii. E1 & E3 iii. E1 & E4 iv. E2 & E3 V. E2 & E4 vi. E3 or E4 (d) Identify all possible pairs of events defined in part (b) that are mutually exclusive. (3 marks) (e) Verify mathematically that E2 and E4 are independent events, while E3 and E4 are not. (3 marks) 2. Suppose we select a random sample of 4 numbers between 1 and 30, sampling without replacement. (a) How many samples of size 4 are possible? (2 marks) (b) What is the probability that the sum of the values in our sample is less than 14? (3 marks)