<s>[INST] Here is a problem I'm not certain how to approach:

Suppose that a fair coin is flipped several times but we don't know the probability of getting either heads or tails. Instead, each time the coin is flipped, an outcome is obtained which, with equal probability--call it \(p\)--can be either the actual outcome of the coin flip or a random value, either heads or tails with equal probability.

How do we deal with this?[/INST]