It is well documented that people are not very good at generating random sequences. However, is it possible that two people, working independently, could generate randomness together? Consider the following two examples:

Example 1
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My wife and I can't decide where to go to dinner, and we've narrowed it down to two options. Neither of us has a coin to flip, so we decide on this: My wife will choose a number between 1 and 1000. I will choose, privately, that we will go to Option A if her number, say, ends in an odd number. If she is unaware of my choice, and I am unaware of hers, will our selection be random?

Example 2
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We need to randomly select a name from a list of length *n*. Person 1 decides on an order for the names: perhaps ordering alphabetically by the second letter of the last name. Person 2 "randomly" chooses a number from 1 to *n*. Would that selection be random?