Question

A multiple choice test has 10 questions. Each question has four answer choices.

a. What is the probability a student randomly guesses the answers and gets exactly six questions correct?

b. Is getting exactly 10 questions correct the same probability as getting exactly zero correct? Explain.

c. Describe the steps needed to calculate the probability of getting at least six questions correct if the student randomly guesses. You do not need to calculate this probability!

Answer 1

a.

`((10)/(6))*((1)/(4))^6 *((3)/(4))^1^0^-^6=0.0162`

0.0162 = 1.62%

So, there is a 1.62% chance that a student will randomly guess and get exactly six questions correct.

b.

No, getting exactly 10 questions correct is not the same probability as getting exactly zero correct. It is assumed that each question gives four answer choices, three of which will be wrong. Because of this, you are three times more likely to guess all of the answers incorrectly.

However, if it were a test where all the questions were either true or false, the probability would be the same.

c.

In order to calculate the probability of getting at least six questions correct when randomly guessing, you would need to find the probabilities of the student getting exactly 6, 7, 8, 9, and 10 questions correct. After doing that, add all the answers together. What you get is the probability of guessing at least six answers correctly.

Answer 2

In a multiple choice question the probability of success is : p = 1/4 = 0.25
and the probability of failure is : q = 3/4 =) 0.75
r = 6 ( correct answers )
Probability = 10 C r * ( 1/4 ) ^(10- r) * ˙( 3/4 )^r =
= 10 C 6 * ( 0.25 )^4 * ( 0.75 )^6 =
= 210 * 0.00390625 * 0.1779785 =
= 0.145998
Answer: Probability is 0.145998 or 14.5998 %.