positiveeast.org->Probability-and-statistics-> SOLUTION: A) A test consists of 10 true and false questions. To pass the test a student must answer at least eight questions correctly. If the student guesses on each questions what is the var visible_logon_form_ = false;Log in or register.Username: Password: Register in one easy step!.Reset your password if you forgot it.”; return false; } “> Log On

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Click here to see ALL problems on Probability-and-statisticsQuestion 296701: A) A test consists of 10 true and false questions. To pass the test a student must answer at least eight questions correctly.

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If the student guesses on each questions what is the probability that the student will pass the test? Found 2 solutions by stanbon, Theo:Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website! A test consists of 10 true and false questions. To pass the test a student must answer at least eight questions correctly. If the student guesses on each questions what is the probability that the student will pass the test?—Binomial Problem with n = 10 and p = 1/2—P(8= 0.0547..===================Cheers,Stan H. Answer by Theo(11696) (Show Source): You can put this solution on YOUR website! Assume it was only 3 answers on the test and the student needed to get at least 2 out of 3 correct.Probability of getting exactly 0 wrong would be .5^3 = .125 * 1 = .125Probability of getting exactly 1 wrong would be .5^3 = .125 * 3 = .375Probability of getting exactly 2 wrong would be .5^3 = .125 * 3 = .375Probability of getting exactly 3 wrong would be .5^3 = .125 * 1 = .125Total probability is equal to 1 as it should be.Probability of getting 0 or 1 wrong would be .375 + .125 = .5Since 0 or 1 wrong is the same as getting 2 or 3 right, then this is the probability that the student will get at least 2 right.The individual probabilities are multiplied by the number of ways they can occur.If we let 0 = wrong and 1 = correct, then:You can get 0 wrong only 1 way (111)You can get 1 wrong 3 ways (110) (101) (011)You can get 2 wrong 3 ways (001) (010) (100)You can get 3 wrong 1 way (000)The same concept applies to the larger numbers.—–With 10 answers, this is what happens:p(0) = probability of getting exactly 0 correct.p(1) = probability of getting exactly 1 correct.etc.p(0) = .5^10 = .000976563 * 1 = .000976563p(1) = .5^10 = .000976563 * 10 = .009765625p(2) = .5^10 = .000976563 * 45 = .043945313p(3) = .5^10 = .000976563 * 120 = .1171875p(4) = .5^10 = .000976563 * 210 = .205078125p(5) = .5^10 = .000976563 * 252 = .24609375p(6) = .5^10 = .000976563 * 210 = .205078125p(7) = .5^10 = .000976563 * 120 = .1171875p(8) = .5^10 = .000976563 * 45 = .043945313p(9) = .5^10 = .000976563 * 10 = .009765625p(10) = .5^10 = .000976563 * 1 = .000976563Total probability equals 1 as it should.Probability of getting 0 or 1 or 2 wrong is equal to:.000976563 + .009765625 + .043945313 = .0546875Since the probability of getting 0 or 1 or 2 wrong is the same as the probability of getting 8 or 9 or 10 right, then the probability that the student will get at least 8 correct is equal to .0546875.The number of ways each percentage can be achieved is given by the formula:For example, with 10 answers, the number of ways of getting exactly 4 wrong is equal to:With 10 answers, the number of ways of getting exactly 6 wrong is the same as getting exactly 4 wrong as shown below:

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