A student has 3 exams.The probability that he does "well" on his first exam is 80%.However,his performance on the remaining two exams depends on how "well" he did on the previous exam.The probability of doing "well" on an exam is 95% if the previous exam was done "well",but only 50% if the previous was not done "well".What is the probability he does "well" on exactly 2 of his 3 exams?
A)15.3%
B)27.8%
C)32.7%
D)38.4%

Question

Quizplus · Accepted Answer

The probability of doing well on the first exam is 80%. The probability of doing well on the second exam if the first exam was done well is 95%. The probability of doing well on the second exam if the first exam was not done well is 50%. The probability of doing well on the third exam if the second exam was done well is 95%. The probability of doing well on the third exam if the second exam was not done well is 50%.The probability of doing well on exactly 2 of the 3 exams is:P(well on first exam) * P(well on second exam | well on first exam) * P(not well on third exam | well on second exam) + P(well on first exam) * P(not well on second exam | well on first exam) * P(well on third exam | not well on second exam) = 0.8 * 0.95 * 0.05 + 0.8 * 0.05 * 0.95 = 0.153

A Student Has 3 Exams