Question

A multiple choice test has 7 questions. Each question has 4 choices with only 1 correct answer for each. What is the probability of getting exactly 5 questions correct

Answer 1

`(9)/(16384)`

Explanation:

I presumed this question is referring to the probability of getting 5 questions right and 2 wrong.

Since each question is independent of each other, you just have to multiply the probability of getting a question right 5 times then multiply that by the probability of getting the last questions wrong twice.

The probability of a correct answer is
`(1)/(4)`

The probability of a wrong answer is
`(3)/(4)`

So the probability of getting just 5 right is...

`(1)/(4)`*
`(1)/(4)`*
`(1)/(4)`*
`(1)/(4)`*
`(1)/(4)`*
`(3)/(4)`*
`(3)/(4)`=
`(9)/(16384)`