A multiple choice test has 10 questions, each of which has 4 possible answers

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Binomial probability:

The probability of getting exactly x successes out of n trials, when
the probability of getting 1 success in 1 trial is p is given by the
formula 
.

Notice that 
 is also written as nCx or C(n,x) or
the number of combinations of n things taken x at a time.

This can also be found with a TI-83 or 84 graphing calculator, press
2ND VARS to find binompdf(n,p,x). Put in numbers for n,p, and x.

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?

That's the binomial probability of getting exactly 6 successes in 10 trials with
the probability of 1 success in 1 trial of 1/4.

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

No.  Although both are very unlikely, it is 3 times as likely to guess an answer
incorrectly than to guess it correctly.  So it is more likely to guess them all
incorrectly than all correctly.  (However, in a true-false test, they would be
the same.)   

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!

You would do these steps:

1. Calculate the probability of getting exactly 6 correct.

2. Calculate the probability of getting exactly 7 correct.

3. Calculate the probability of getting exactly 8 correct.

4. Calculate the probability of getting exactly 9 correct.

5. Calculate the probability of getting all 10 correct.


Then you would add them all up and you'd get: .0197277069

Edwin

See the Compromises/Disruptions in the Testing Process—Limitation of Remedies section of ACT's Terms and Conditions for remedies available to examinees affected by compromises or disruptions in the testing process.

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