Question

. In a history class, Colin and Diana both write a multiple choice quiz. There are 10 questions. Each question has five possible answers. What is the probability that Passing is considered 70%

a) Colin will pass the test if he guesses an answer to each question.

b) Diana will pass the test if she studies so that she has a 75% chance of answering each question correctly.

Answer 1

a) p = 1/5 = 0.2

n = 10

P(X > 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

              = 10C7 * 0.2⁷ * 0.83³ + 10C8 * 0.2⁸ * 0.83² + 10C9 * 0.2⁹ * 0.83¹ + 10C10 * 0.2¹⁰ * 0.83⁰

              = 0.0009

b) p = 0.75

n = 10

P(X > 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

              = 10C7 * 0.75⁷ * 0.25³ + 10C8 * 0.75⁸ * 0.25² + 10C9 * 0.75⁹ * 0.25¹ + 10C10 * 0.75¹⁰ * 0.25⁰

              = 0.7759