We can use Binomial distribution to calculate the probability of exactly 4 success
There are 8 questions which is our trial
Probability of succes (p)
Since in every question, there is 4 options with one right answer, then probability of success (p) = 1/4 = 0.25
probabiliti of failure (q) = 1- p = 1- 0.25 = 0.75
We will now use the formula below
[tex]p(x)^{}=^nC_xP^xq^{n-x}[/tex]
substitute the values into the formula
[tex]p(x=4)=^{8\text{ }}C_4(0.25)^4(0.75)^{8-4}[/tex][tex]=\frac{8!}{(8-4)!4!}.(0.25)^4.(0.75)^4[/tex][tex]=\frac{8!}{4!4!}\text{.}(0.25)^4(0.75)^4[/tex][tex]=\frac{8\times7\times6\times5\times4!}{4\times3\times2\times1\times4!}\times(0.25)^4\times(0.75)^4[/tex][tex]=\frac{1680}{24}\times(0.00390625)\times(0.31640625)[/tex][tex]\approx0.087[/tex]
