Problem 15. The correct answer is (A).

Imagining to complete the extraction of the 90 numbers, emptying the entire urn, the indicated event occurs if and only if the 90th number drawn is one of the 4 that are present in both cards. The probability that this happens is equal to $\frac{4}{90}=\frac{2}{45}$. It is irrelevant whether the extraction of this 90th number occurs chronologically last or not (or even first): there are still 4 favorable cases out of 90.
15. Lucia and Carla are playing bingo against each other (with no other opponents). Each has a card with 15 numbers; the two cards have exactly 4 numbers in common. What is the probability that, after 89 numbers have been drawn, neither of them has yet completed a bingo?
(A) $2 / 45$
(B) $3 / 89$
(C) $1 / 15$
(D) $1 / 30$
(E) $1 / 90$