Question 1008087: A history quiz had 8 multiple choice questions. Each question has 4 answer choices. A student has forgotten that the quiz was to tale place and guesses at all of the answers.
a) Find the probability that the student gets exactly 5 of the 8 questions correct.
b) Find the probability that the student gets at least 6 questions correct.
Found 2 solutions by stanbon, Boreal:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A history quiz had 8 multiple choice questions. Each question has 4 answer choices. A student has forgotten that the quiz was to tale place and guesses at all of the answers.
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Binomial Problems with n = 8 and P(correct) = 1/4
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a) Find the probability that the student gets exactly 5 of the 8 questions correct.
P(x = 5) = 8C5*(1/4)^5*(3/4)^3 = binompdf(8,1/4,5) = 0.0231
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b) Find the probability that the student gets at least 6 questions correct.
P(6<= x <=8) = 1 - binomcdf(8,1/4,5) = 0.0042
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Cheers,
Stan H.
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Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! it is 8C5(0.25)^5(0.75)^3=0.0231
For at least 6, we need 6,7,8
6: 8C6(0.25^6)(0.75^2)=0.0038
7: 8(0.25^7)*0.75=0.0008
for 8, 0.25^8=0.00002
The probability is 0.0046.
The expected value is 2 with the variance 1.5.
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