Question

. An instructor is considering different possible styles for an upcoming quiz. In each case, calculate the probability that a student just guessing gets at least 70% of the quiz correct: (a) The quiz has ten questions that are all answered “True” or “False.” (b) The quiz has ten questions, multiple choice, with choices (a), (b), (c), or (d) (c) The quiz has ten questions, multiple choice, with choices (a), (b), (c), (d), or (e) (d) The quiz requires the student to match 10 terms with their correct definitions, where exactly 10 definitions are given. (e) The quiz requires the student to match 10 terms with their correct definitions, where 15 definitions are given and five of the definitions do not match any of the terms.

Answer #1

(a) There are ^{10}C_{7} ways to pick 7
questions that he answers correctly by guessing and he has
probability 1/2 of guessing correctly on each question, so the
probability that he guesses exactly seven answers correctly is

Similarly, the probability that exactly 8/9/10 answers correctly. THen, the probability that at least 7 answers correctly should be follows binomial distribution with n=10, p=1/2

(b) The quiz has ten questions, multiple choice, with choices (a), (b), (c), or (d). Then only p is change

p=1/4

THen, the probability that at least 7 answers correctly should be follows binomial distribution with n=10, p=1/4

(c) Here p=1/5

(d) Here p=1/10

(e) Here p=1/15

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