Question

Richard has been given a 12-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to answer a question correctly. Assuming that Richard guesses on all 12 questions, find the probability that he will answer no more than 3 questions correctly. Round your answer to the nearest thousandth.

Question7 Richard has been given a 12-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not aswers yuestion corely,Asuming that Richard gucses on all 12 uestions, find the probability tht he will answer no more than 3 questions Not yet answered Points out of 4.00P Flag question any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to questions correctly. Round your attended the class rocently, he doesn't know answer a question co answer to the nearest thousandth. Assuming Select one: a. 0.25 b. 0.258 С. 0.063 d. 0.5 e. 0.649

Answer 1

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This is a problem of using binomial distributoin.

The probability of getting an answer right is 1/4 as there are 4 options of which 1 is correct.

So, P(getting no more than 3 questions correctly) [we have used binomial distribution here to solve this problem]
= P(X<=3) = P(X=0, 1, 2, 3)
= 12C0*(1/4)^0 *(3/4)^12 + 12C1*(1/4)^1 *(3/4)^11+12C2*(1/4)^2 *(3/4)^10+12C3*(1/4)^3 *(3/4)^9

= 0.6488