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 wil

Question

3 years ago

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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 wil

l 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.)

Mathematics

1 answer:

algol13 · Answer 1 · 2022-01-17T18:05:03+03:00

Answer:

P(Topic A) = 0.91

P(Topic B) = 0.9163

The student should choose Topic B to maximize the probability of writing a good paper because P(Topic B)>P(Topic A).

Step-by-step explanation:

If Topic A is chosen, 2 books will be ordered (n=2)

If topic B is chosen, 4 books will be ordered (n=4)

Probability that a book arrives in time (p) = 0.7

Probability that a book does not arrive in time (q) = 1 - p = 1 - 0.7 = 0.3

We will <u>use the binomial distribution</u> to find out which topic should the student choose to maximize the probability of writing a good paper. The binomial distribution formula is:

P(X=x) = ⁿCˣ pˣ qⁿ⁻ˣ

where p = probability of success

q = probability of failure

n = total no. of trials

x = no. of successful trials

For Topic A, n = 2, p=0.7 and q=0.3. If topic A is chosen, the student will use at least half the books i.e. he will use either 1 or 2 books. So,

P(Topic A) = P(X=1) + P(X=2)

=²C₁ (0.7)¹(0.3)²⁻¹ + ²C₂ (0.7)²(0.3)²⁻²

= 0.42 + 0.49

P(Topic A) = 0.91

For topic B, n=4, p=0.7 and q=0.3. If topic B is chosen, the student will choose 2 or more books i.e. 2, 3 or 4 books.

P(Topic B) = P(X=2) + P(X=3) + P(X=4)