Suppose that on a true/false exam you have no idea at all

Last updated: 7/10/2022

Suppose that on a true/false exam you have no idea at all about the answers to three questions. You choose answers randomly and therefore have a 50-50 chance of being correct on any one question. Let CCW indicate that you were correct on the first two questions and wrong on the third, let WCW indicate that you were wrong on the first and third and correct on the second, and so forth. Then S = {CCC, CCW, CWC, WCC, CWW, WCW, WWC, WwW) is the sample space of all possible sequences of correct and incorrect responses on your part. (1) Let E₁ be the event that exactly one answer is correct. (i) Write E₁ as a set in the set-roster notation: E₁ = { (ii) What is the probability of E₁? (2) Let E₂ be the event that at least two answers are correct. (i) Write E₂ as a set in set-roster notation: E₂ = { (ii) What is the probability of E2? }