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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

Question 5 1 PointA Student Takes A Multiplechoice Test With 8 Questions On It Each Of Which Have 4 Choices The Student Randomlyguesses An Answer To Each Questi class=

Sagot :

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]

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