Binomial Distribution Problem

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 inter library loan,whereas if topic B is chosen,the student will order four books. The student believes thata good paper necessitates receiving and usingat leastt half the books ordered for either topic chosen.If the probability that a book ordered through inter-library loan actually arrives in time is .9 andbooks arrivee independently of one another,whichtopic shouldd the student choose to maximize the probability of writing a good paper?

How do I approach this? Do I need to use the Bayes formula? Here is the answer:

For p= .9, the probability is higher for B (0.9963 vs 0.99 for A)

Say she chooses topic A. She needs at least one book to arrive on time. The probability that no books arrive on time is 0.1 x 0.1 = 0.01 so the probability that at least one book arrives on time is 1 - 0.01 = 0.99.

Say she chooses topic B. She needs at least two books to arrive on time. The probability of no books arriving on time is 0.1 x 0.1 x 0.1 x 0.1 = 0.0001. The probability of exactly one book arriving on time is 4 x 0.1 x 0.1 x 0.1 x 0.9 = 0.0036 (binomial probability distribution formula - the 4 comes from 4C1). So the probability of her not getting enough books is 0.0001 + 0.0036 = 0.0037 and the probability she does get the books she needs on time is 1 - 0.0037 = 0.9963.

So she should choose topic B.