Question

On a certain statistics exam, there are 9 multiple choice questions. Each question has 5 possible answers to choose from (and only 1 correct answer). Suppose you didn’t study at all and are planning on guessing the correct answer for each question.

Therefore, the probability of guessing a question correctly is ___________ . (Round to two decimals)

  Let X = number of questions the student guesses correctly

(Round all answers to four decimals)

a)      What’s the probability you guess at least one question correctly?

b)      What’s the probability you guess strictly less than half of the questions correctly?

c)      What’s the expected number of questions you guess correctly?

d)     What’s the probability of guessing between 2 and 7 questions (inclusive) correctly?

Answer 1

A standard problem on Binomial probability distribution.

The probability of guessing a question correctly is 1/5.

(5 options to choose from, exactly one correct)

a)      For n = 5, p = 1/5

b) You can guess a maximum of 4 questions correctly.

c)      By standard formula,

If you are looking for the closest integer value, quite obviously it is 2

d)     Repeating the process