# On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. Find the probability that a student guesses at least 2 answers correctly. Give the formula or calculator function used. Show work of how you got your answer.

###### Question:

answers, one of

which is correct. Find the probability that a student guesses at least 2 answers

correctly.

Give the formula or calculator function used. Show work of how you got your

answer.

## Answers

Using the binomial distribution, it is found that there is a 0.9499 = 94.99% probability that a student guesses at least 2 answers correctly.--------------------------For each question, there are only two possible outcomes, either the student guesses the correct answer or not. The probability of guessing the correct answer on a question is independent of any other question, which means that the binomial distribution is used to solve this question.Binomial probability distribution [tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex] [tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]x is the number of successes.n is the number of trials. p is the probability of a success on a single trial. One of the four options is correct, thus [tex]p = \frac{1}{4} = 0.25[/tex]17 questions, thus [tex]n = 17[/tex]The probability of at least 2 correct is:[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]In which[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]Then[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex][tex]P(X = 0) = C_{17,0}.(0.25)^{0}.(0.75)^{17} = 0.0075[/tex][tex]P(X = 1) = C_{17,1}.(0.25)^{1}.(0.75)^{16} = 0.0426[/tex][tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0075 + 0.0426 = 0.0501[/tex][tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.0501 = 0.9499[/tex]0.9499 = 94.99% probability that a student guesses at least 2 answers correctly.A similar problem is given at https://brainly.com/question/15019040