Are these two sample approaches equally random? I have a collection of words, and I want to choose one of them randomly. I can sample the collection and get a word as the result. I can also do this: 1. Take first word as the result. 2. For every word, flip a coin, and choose whether to skip it or overthrow the result. After iterating over the whole collection, I will have randomly selected a word. Are these two strategies equivalent in terms of unbiased randomness?

Following my short exchange with @Presage:

Suppose you have the words $w_1, w_2, \dots, w_n$. Then, for $1\le i\le n$, we have:
The probability of choosing $w_i$ with the first method is $\frac1n$. The probability of choosing $w_i$ with the second method is equal to $\dfrac1{2^{n-i+1}}$.