Problem 1 Imagine that you walk into some class on the Thursday morning after Mardi Gras...

Problem 1 Imagine that you walk into some class on the Thursday morning after Mardi Gras break and are surprised to discover that a ten-question, multiple choice quiz is being conducted. You have not studied for this quiz, so you decide to answer the questions randomly. Determine the following:

a) If each question has four possible responses (a, b, c, or d), then how many possible ways can you respond to the quiz?

b) How probable is it that you will score a 0% on the quiz?

c) How probable is it that you will earn an A grade on the quiz (90% or higher)?

Solutions

Expert Solution

Total problems = 10

Number of possible options per problem = 4

a) Total ways = 4¹⁰ = 1048576, because each question we can answer in 4 ways. That's why total ways to answer is 4¹⁰ or 1048576.

b) To get 0% we need to get all questions wrong. In each question there are 1 correct option and 3 incorrect options.

So, to get 0% we need to select from those 3 incorrect option.

Hence total ways = 310 = 59049.

So, P(0%) =

Hence probability to score 0% is 59049/1048576 or 0.0563 (approx.)

c) For A we need 90% or higher implies either 9 questions are correct or all 10 questions are correct.

Total ways for 9 answers =

to select the 1 problem which is getting wrong, 3 because that question can be answered wrong in 3 ways and 1⁹ because rest questions can be answered by 1 way only.

Total ways for 10 correct answers = 1

Hence P(A grade) =

Hence probability of getting an A is 31/1048576 or 0.00003.

Please comment if any doubt. Thank you.

orchestra answered 1 year ago

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