Question

A statistics test has 4 multiple choice questions with 4 choices with one correct answer foreach. If we just randomly guess on each of the 4 questions, what is the probability that youget exactly 3 questions correct?

Answer 1

We need to use a binomial distribution formula to determine the probability, the formula is:

`B(X\colon n,p)=(nCx)(p^x)(1-p)(n-x)`

Where "n" is the total number of questions, in this case, 4 questions

"p" is the probability of getting one question right. Since each question has 4 choices and there is only one right question, the probability "p" is:

`p=(1)/(4)=0.25`

"x" is the number of questions we want to get right, in this case, 3. Replacing the values we get:

`B(X\colon4,0.25)=(4C3)(0.25)^3(1-0.25)(4-3)`

Solving the operations:

`B(X\colon4,0.25)=(4)(0.015625)(0.75)(1)`
`B(X\colon4,0.25)=0.047`

Therefore, the probability is 0.047.