Question 677138: A test consists of 25 multiple-choice questions. Assume that a test taker randomly guesses a choice for each and every question. Clearly state what probability model(s) you use and what value each parameter is equal to.
1 (10 points). If each and every question has 3 choices (one correct, two incorrect), what is the probability that the test taker will get a B or better (i.e., 80 points or higher)?
2 (10 points). If fifteen questions has three choices each (one correct, two incorrect) and ten has two choices each (one correct, one incorrect), what is the probability that the test taker will get a B or better?
I used the Binomial Probability equation (n!/(k!(n-k)!)*(p^k)*(1-p)^(n-k) for the first problem and it looks as if it works, however I don't think that this equation applies to the second question. Any suggestions?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A test consists of 25 multiple-choice questions. Assume that a test taker randomly guesses a choice for each and every question. Clearly state what probability model(s) you use and what value each parameter is equal to.
1 (10 points). If each and every question has 3 choices (one correct, two incorrect), what is the probability that the test taker will get a B or better (i.e., 80 points or higher)?
Binomial Problem with n = 25 ; p(correct) = 1/3 ; p(incorrect) = 2/3
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Note: 80% of 25 = 20
P(x >- 20) = 1 - binomcdf(25,1/3,19) = 0.000002269
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2 (10 points). If fifteen questions has three choices each (one correct, two incorrect) and ten has two choices each (one correct, one incorrect), what is the probability that the test taker will get a B or better?
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Need 20 correct out of 25 ; same as miss 5 or less out of 25
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P(x <= 5 wrong) means
5 wrong from 15 and 0 wrong from 10::::15C5(2/3)^5*(1/3)^10*10C0(1/2)^10
or 4 wrong from 15 and 1 wrong from 10::::15C4(2/3)^4(1/3)*10C1(1/2)10
or 3 wrong from 15 and 2 wrong from 10etc
or 2 wrong from 15 and 3 wrong from 10
or 1 wrong from 15 and 4 wrong from 10
or 0 wrong from 15 and 5 wrong from 10
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Add those products to get P(less than or equal to 5 wrong)
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Cheers,
Stan H.
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