Question

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.

Answer 1

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.

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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  

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$  

$C_{n,x} = \frac{n!}{x!(n-x)!}$

• 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 $p = \frac{1}{4} = 0.25$
• 17 questions, thus $n = 17$
• The probability of at least 2 correct is:

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

Then

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{17,0}.(0.25)^{0}.(0.75)^{17} = 0.0075$

$P(X = 1) = C_{17,1}.(0.25)^{1}.(0.75)^{16} = 0.0426$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.0075 + 0.0426 = 0.0501$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.0501 = 0.9499$

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