Question 995499: Beth is taking a ten-question multiple-choice test for which each question has three answer choices, only one of which is correct. Beth decided on answers by rolling a fair die and marking the first answer choice if the die shows 1 or 2, the second if it shows 3 or 4, and the third if it shows 5 or 6. Find the probability of
a) exactly four correct answers
b) fewer than three correct answers
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Beth is taking a ten-question multiple-choice test for which each question has three answer choices, only one of which is correct. Beth decided on answers by rolling a fair die and marking the first answer choice if the die shows 1 or 2, the second if it shows 3 or 4, and the third if it shows 5 or 6.
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Binomial Problem with n = 10 and p(correct) = 1/3
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Find the probability of
a) exactly four correct answers
P(x = 4) = 10C4(1/3)^4*(2/3)^6 = binompdf(10,1/3,4) = 0.2276
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b) fewer than three correct answers
P(0<= x <= 2) = binomcdf(10,1/3,2) = 0.2991
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Cheers,
Stan H.
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