Question

Selve the problem. (Spts.) 9) Multiple-choice questions on a test each have 6 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions. a. Use the multiplication rule to find the probability that the first 2 guesses are wrong and the last 3 guesses are correct and W denotes a wrong answer 9) . That is, find P(WWCCC), where C denotes a correct answer b. Make a complete list of the different possible arrangements of 2 wrong answers and 3 correct answers, then find the probability for each entry in the list. C. Based on the preceding results, what is the probability of getting exactly 3 correct answers when 5 guesses are made?

Answer 1

a It is given that each question has 6 possible answers. P[correct answer] = 1/6 P[correct answer] = 5/6 because Each question is independent i.e. P[w w c c c] = P(w). P(w). P(c). P(c). P(c) = 5/6. 5/6/. (1/6)^3 = 5/7776 = 0.0032 c let us define on indicator function x_1 = { 1: correct answer is made 0: wrong answer is made P[c] = 1/6 = p, p(w) = 5/6 = 1 - p = q y = sigma^5_i = 1 xi = No of correct answer in 5 guesses y tilde Binomial (5, 1/6) P[Y =y] = 5_cy (1/6)^y (5/6)^5 - y: y = 0, 1, 2 5 P[y = 3] = 5_C 3 (1/6)^3 (5/6)^2 = 0.03215