Question

Multiple-Choice Exam A student takes a 13-question, multiple-choice exam with two choices for each question and guesses on each question. Find the probability of guessing at least 9 out of 13 correctly. Assume the variable is binomial. Round the intermediate and final answers to three decimal places. P (guessing at least 9 out of 13 correctly) = x

Answer 1

Solution :

=> From the given information,

=> P(success) = p = 1/2 = 0.5

=> q = 1 - p = 0.5

=> From binomial distribution, P(X = r) = nCr*p^r*q^(n-r)

=> P(X >= 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13)

= 13C9*0.5^9*0.5^4 + 13C10*0.5^10*0.5^3 + 13C11*0.5^11*0.5^2 + 13C12*0.5^12*0.5^1 + 13C13*0.5^13*0.5^0

= 0.0873 + 0.0349 + 0.0095 + 0.0016 + 0.0001  

= 0.1334

= 0.133 (rounded)

=> P(guessing at least 9 out of 13) = 0.133

Answer 2

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