SOLUTION: A multiple choice exam contains 50 questions. Each question has 5 choices, one of which is correct. We are interested in knowing the probability guessing exactly 18 questions corr

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Question 600644: A multiple choice exam contains 50 questions. Each question has 5 choices, one of which is correct. We are interested in knowing the probability guessing exactly 18 questions correctly.

(a) Is this a binomial experiment? Explain how you know.
(b) Use the correct formula to find the probability of guessing exactly 18 questions correctly out of the 50 questions. Show your calculations or explain how you found the probability
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)
Is this a binomial experiment? Yes

Explain how you know. Each guess at a question has two possible outcomes: A success (you get the question correct) or a failure (you get the answer wrong). Each guess is also independent of any other guess (assume that each question is unrelated to the other...ie no one question depends on another)


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b)

P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x)

P(X = 18) = (50 C 18)*(0.2)^(18)*(1-0.2)^(50-18)

P(X = 18) = (50 C 18)*(0.2)^(18)*(0.8)^(50-18)

P(X = 18) = (18053528883775)*(0.2)^(18)*(0.8)^32

P(X = 18) = (18053528883775)*(0.000000000000262144)*(0.00079228162514264337593543950336)

P(X = 18) = 0.00374957125234


So the probability of guessing exactly 18 questions correctly is approximately 0.00374957125234