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) STAT 151 i. ii. iii. iv. (c) List all possible outcomes and find the probabilities of the following events. (12 marks: 2 for each) i. ii. iii. iv. E1 = {Exactly 1 person of type L is drawn} E2 = {The second person is right handed} E3 = {At MOST one person is ambidextrous} E4 = {Both people have the same handedness} V. vi. Not E3 E1 & E3 E1 & E4 E2 & E3 E2 & E4 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) 1