Final answer:
In a sample of size 64, the probability of selecting the same object twice without replacement is 0, because once an object is selected, it's no longer in the sample to choose again.
Step-by-step explanation:
The question pertains to the concept of sampling without replacement from a statistical perspective. In sampling without replacement, once an object is selected from a set, it cannot be chosen again. Given a random sample of size 64, the probability of selecting the same object twice without replacement is actually 0 because once you have selected an object, it's no longer available to be selected again. Therefore, options a) 1/32, b) 1/64, c) 1/128, d) 1/256 are all incorrect because they suggest there is a possibility of selecting the same object again, which is not the case without replacement.
In other words, when you choose one item out of 64, you have 64 options for the first pick. For the next pick, there are only 63 items left, so you have a 0 chance of picking the same item because it has already been removed from the set. This concept is crucial to understand in probability and combinatorics, especially when calculating the probabilities of various events in a finite discrete space.