Question

What is the probability that Sue gets a B grade of at least 4 out of 5 on a 5-question multiple choice test (with answers A - D for each question) by guessing at random? What is the sample space? What are the events that satisfy the condition of at least 4 out of 5 correct answers?

Answer 1

The total number of questions is: 5 The number of possible choices is: 4 (A, B, C, D) The answer choice is ordered: A to D The total sample space is, Here the order is important, so, we apply permutation rule, 5! P45 -4)! 120 1 = 120 Hence, the total sample space events is: 120 Calculate the probability that Sue gets B grade of at least 4 out of 5. The probability of choosing correct option is: - = 0.25 P(4out of 5)=P(X = 4)+P(X = 5) = )(0.25)*(1+0.75)*4+ (3)(0.25)' (1–0.75)'s = 0.014648 +0.000977 = 0.015625