A student who is trying to write a paper for a course has a choice of two topics

Question

A student who is trying to write a paper for a course has a choice of two topics, A and B. If topic A is chosen, the student will order two books through interlibrary loan, whereas if topic B is chosen, the student will order four books. The student believes that a good paper necessitates receiving and using at least half the books ordered for either topic chosen. If the probability that a book ordered through interlibrary loan actually arrives in time is 0.7 and books arrive independently of one another, which topic should the student choose to maximize the probability of writing a good paper? (Enter your answers to four decimal places.) For topic A, P(at least half received) = For topic B, P(at least half received) = Therefore, the student should choose Which topic should the student choose if the arrival probability is only 0.6 instead of 0.7? (Enter your answers to four decimal places.) For topic A, P(at least half received) = For topic B, P(at least half received) = Therefore, the student should choose

Explanation / Answer

1st case
for topic A = 0.7*0.3 +0.7*0.7 = 0.7
for topic B = 0.7^4 +0.7^3*0.3+0.7^2+0.3^2 = 0.3871

so student must choose topic A

2nd case
for topic A = 0.6*0.4 +0.6*0.6 = 0.6
for topic B = 0.6^4 +0.6^3*0.4+0.6^2+0.4^2 = 0.2736

so student must choose topic A

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