A multiple choice exam has five possible answers per question. Only one of those

Question

A multiple choice exam has five possible answers per question. Only one of those five answers is the correct answer. A student, who did not prepare for the test, answers the exam randomly and in order, starting from the first question. a. What is the probability that the first question he answered correctly is the second question? b. What kind of distribution is it if we are interested in the order of the first questions he answers correctly? Justify. c. What is the probability that none of the first three questions is answered correctly? d. What is the probability that the first correct answer he gets is somewhere after the second question?

Explanation / Answer

here probability of gussing correctly =1/5 =0.2 (as thre are 5 choices)

a) probability that the first question he answered correctly is the second question =P(first wrong and second right)

=0.8*0.2 =0.16

b) this should be gqometric distribution with parameter p=0.2

c)  probability that none of the first three questions is answered correctly =(0.8)3 =0.512

d)  probability that the first correct answer he gets is somewhere after the second question

=P(first 2 answer incorrect) =(0.8)2 =0.64

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