SOLUTION: Six questions are in a multiple choice quiz. Each question has 5 possible answers. A student guesses at each question.
b)Find the probability that the student passes (earns at lea
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b)Find the probability that the student passes (earns at lea
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Question 1194087: Six questions are in a multiple choice quiz. Each question has 5 possible answers. A student guesses at each question.
b)Find the probability that the student passes (earns at least 50%)
c)What is the student's expected number of correct answers? Answer by ikleyn(52847) (Show Source):
You can put this solution on YOUR website! .
Six questions are in a multiple choice quiz. Each question has 5 possible answers.
A student guesses at each question.
a) Find the probability that the student passes (earns at least 50%)
b) What is the student's expected number of correct answers?
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Answering randomly, the probability to answer each separate multiple choice question correctly is ;
answering incorrectly is .
The answers to 6 questions of the quiz are independent events.
So, we have a binomial distribution with 6 trials; the probability of success is = 0.2 in each
individual trial and the problem asks in part (a) about probability of 3 or more success trials.
The formula is
P = P(3) + P(4) + P(5) + P(6) = = .
It can be calculated manually, or using technology.
To facilitate calculations, I used online calculator at this site https://stattrek.com/online-calculator/binomial.aspx
It provides nice instructions and a convenient input and output for all relevant options/cases.
The resulting number is P = 0.09888 (rounded).
It is the ANSWER to question (a).
For question (b), math expectation of binomial distribution is E = n*p = 6*0.2 = 1.2.
