Question 12 (v) - End-of-Chapter Exercises - Chapter 7 - The Mathematics of Maybe: Introduction to Probability

Transcript

Question 12 (v) Write the sample space and calculate the probability based on the given information. (v) A student takes a multiple-choice test with 3 questions, each having 4 options (A, B, C, D), with only one correct answer. What is the probability that the student guesses and gets exactly 2 answers correct? Now, Probability of guessing right (R) is 1/4 Probability of guessing wrong (W) is 3/4 To get exactly two right, the outcomes could be: (R, R, W), (R, W, R), or (W, R, R) Now, Probability of (R, R, W) = 1/4 ×1/4 ×3/4=𝟑/𝟔𝟒 Probability of (R, W, R) = 1/4 ×3/4 ×1/4=𝟑/𝟔𝟒 Probability of (W, R, R) = 3/4 ×1/4 ×3/4=𝟑/𝟔𝟒 Thus, Required Probability = Probability of (R, R, W) + Probability of (R, W, R) + Probability of (W, R, R) = 3/64+3/64+3/64 = 𝟗/𝟔𝟒