A student who is trying to write a paper for a course has a choice of two topics
ID: 3276979 • Letter: A
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 0.9 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.)
Which topic should the student choose if the arrival probability is only 0.4 instead of 0.9? (Enter your answers to four decimal places.)
Explanation / Answer
If the probability that a book ordered through interlibrary loan actually arrives in time is 0.9 and books arrive independently of one another, which topic should the student choose to maximize the probability of writing a good paper?
For topic A, P(at least half received) = .1 - =BINOM.DIST(0,2,0.9,TRUE) = 1-0.01=0.99
For topic B, P(at least half received) = .
1 - =BINOM.DIST(1,4,0.9,TRUE) = 1-0.0037=0.9963
Therefore, the student should choose topic B . .
Choose topic B
Which topic should the student choose if the arrival probability is only 0.4 instead of 0.9?
For topic A, P(at least half received) = P(X>=2)=1-P(X<1)
1- =BINOM.DIST(0,2,0.4,TRUE) = 1-0.36=.64
For topic B, P(at least half received) = .P(X>=2)=1-P(X<=1)
1 - =BINOM.DIST(1,4,0.4,TRUE) = 1-0.4752=0.5248
Choose topic A because higher probability.
Hope this will be helpful. Thanks and thumbs up if its help you.
Thanks and God Bless you :)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.