Multiple-choice questions each have four possible answers (a, b, c, d), one of w

Question

Multiple-choice questions each have four possible answers (a, b, c, d), one of which is correct. Assume that you guess the answers to three such questions. a. Use the multiplication rule to find P(WWC), where C denotes a correct answer and W denotes a wrong answer. P(WWC) = (Type an exact answer.) b. Beginning with WWC, make a complete list of the different possible arrangements of one correct answer and two wrong answers, then find the probability for each entry in the list. P(WWC) - see above P(WCW) = P(CWW) = (Type exact answers.) c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made?

Explanation / Answer

P(correct guess) = 1/4 = 0.25

P(C) = 0.25

P(W) = 1 - 0.25 = 0.75

A) P(wwc) = 0.75 * 0.75 * 0.25 = 0.140625

B) p(wwc) = 0.140625

P(WCW) = 0.75 * 0.25 * 0.75 = 0.140625

P(cww) = 0.25 * 0.75 * 0.75 = 0.140625

C) p(exactly one correct answer) = P(wwc) + P(WCW) + P(cww) = 0.140625 * 3 = 0.421875

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.