A 10 question multiple choice exam is given and each

balastantpef

balastantpef

Answered question

2022-02-09

A 10 question multiple choice exam is given and each question has 5 possible answers. A student takes this exam and guesses at every question. What is the probability they get at least 9 questions correct?

Answer & Explanation

iluvyou23452nwj

iluvyou23452nwj

Beginner2022-02-10Added 19 answers

Step 1
Let's first set up the binomial. The general formula is:
k=0nCn, k(p)k((-p)n-k)
We have n=10
With 5 possible answers on each question, this gives the probability of guessing the correct answer p=15, meaning the probability of getting it wrong is -p=45
We're only looking at the probability of getting at least 9 questions correct, and so only care about getting 9 questions correct and 10 questions correct. This gives:
C10, 9159451+C10, 101510450
(10)159451+(1)1510450
=0.00000419844.2×10-6
or roughly 3X more likely than being hit by lightening over the course of a year.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?