Question

Question 5 (1 point)A student takes a multiple-choice test with 8 questions on it, each of which have 4 choices. The student randomlyguesses an answer to each question.What is the probability that the student gets exactly 4 questions correct?Round to 3 decimal places.a0.886b0.9730.0870.208d

Answer 1

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

`p(x)^{}=^nC_xP^xq^(n-x)`

substitute the values into the formula

`p(x=4)=^{8\text{ }}C_4(0.25)^4(0.75)^(8-4)`
`=(8!)/((8-4)!4!).(0.25)^4.(0.75)^4`
`=(8!)/(4!4!)\text{.}(0.25)^4(0.75)^4`
`=(8*7*6*5*4!)/(4*3*2*1*4!)*(0.25)^4*(0.75)^4`
`=(1680)/(24)*(0.00390625)*(0.31640625)`
`\approx0.087`