Final answer:
The probability of failing to draw a spade two times in a row from a 52-card deck with replacement, followed by drawing a spade on the third attempt, is 9/64, which is option B.
Step-by-step explanation:
The question asks about the probability of failing to draw a spade from a well-shuffled deck of 52 cards exactly two times in a row when cards are replaced after each draw. There are four suits (clubs, diamonds, hearts, and spades) in a standard deck with 13 cards each. Since the events of drawing cards are independent (due to replacement), we can multiply the individual probabilities of each draw to get the composite probability.
We calculate the probability of not drawing a spade on the first draw, then drawing a spade on the third draw. The probability of not drawing a spade on a single draw is 39/52 because there are 39 cards that are not spades (clubs, diamonds, and hearts). The second draw is independent and has the same probability of 39/52. On the third draw, the probability of drawing a spade is 13/52 since there are 13 spade cards out of the 52. Therefore, the probability of not drawing a spade twice followed by drawing a spade is (39/52) * (39/52) * (13/52). After simplification, we get 9/64.
So the answer is Option B. 9/64.