You are taking a multiple choice test that has 10 questions

You are taking a multiple-choice test that has five questions. Each of the questions has three answer choices, with one correct answer per question. If you select one of these three choices for each question and leave nothing blank, in how many ways can you answer the questions?

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How many ways can a 10 question multiple
What is the probability that you get exactly 10 questions correct by guessing?
How many possible outcomes are there in answering a 10 item true or false quiz?
What is the probability of answering only 3 questions correctly out of 10 questions which has 4 options each?

You can put this solution on YOUR website!

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

How many ways can a 10 question multiple

Here, there are 4 choices per question, and 10 questions. Choosing an answer for each question is a sequential task, so there are 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4=410 ways to answer.

What is the probability that you get exactly 10 questions correct by guessing?

There is a 0.25 probability of guessing correctly on a 10 question quiz.

How many possible outcomes are there in answering a 10 item true or false quiz?

Required number of ways are 210=1024, because every question may be answered in 2 ways.

What is the probability of answering only 3 questions correctly out of 10 questions which has 4 options each?

The probability that she would still get 3 questions correct is: Solution: There are a total of 4 options. Hence, the probability that the student would randomly select the correct option is 1 / 4. Hence, p = 1 / 4.

Multiple choice questions