Suppose that there were three multiple choice questions on a pop quiz. The first

Question

Suppose that there were three multiple choice questions on a pop quiz. The first question was a true-false question, the second question had three answers, and the third had four. Only one answer was correct for each question. A student did not know how to answer any of the questions and decided to choice an answer randomly.

(c) What is the probability that the student answered one question correctly?

(d) What is the probability that the student got exactly one question right?

(f) What is the probability that the student got at most one question right?

Explanation / Answer

c)probability that the student answered one question correctly=1-P(answer none correctly)=(1/2)*(2/3)*(3/4)

=1-1/4=0.75

d)probability that the student answered exactly one correctly=P(answered first correct*second and third wrong+first and third wrong*second correct+first and second wrong and third right)

=(1/2)*(2/3)*(3/4)+(1/2)*(1/3)*(3/4)+(1/2)*(2/3)*(1/4)=0.4583

e)probability that the student got at most one question right =P(0 question right+exactly one question right)

=0.25+0.4583=0.7083

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