Respuesta :
We need to use a binomial distribution formula to determine the probability, the formula is:
[tex]B(X\colon n,p)=(nCx)(p^x)(1-p)(n-x)[/tex]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:
[tex]p=\frac{1}{4}=0.25[/tex]"x" is the number of questions we want to get right, in this case, 3. Replacing the values we get:
[tex]B(X\colon4,0.25)=(4C3)(0.25)^3(1-0.25)(4-3)[/tex]Solving the operations:
[tex]B(X\colon4,0.25)=(4)(0.015625)(0.75)(1)[/tex][tex]B(X\colon4,0.25)=0.047[/tex]Therefore, the probability is 0.047.
