Resolved: Uniform Events & Bernoulli Events
Why flipping a coin, is not a Bernoulli event. This also has 2 outcomes. we can assign 1 as True (Head) and the other is Not true = False (Tail).
Flipping a coin is indeed a Bernoulli event. It is important to mention, however, that we are talking about a single coin flipping. Then, exactly as you noted, there are two (equiprobable) outcomes - either 'heads' (True / 1) or 'tails' (False / 0).
Additionally, if the coin is unbiased, the probability of getting 'heads' and the probability of getting 'tails' are equal and are exactly 0.5 (if the coin is biased, this can change). This means that there is an equal probability of getting either outcome, so if we define an event A to be "flipping a fair coin", this event is indeed going to have a uniform distribution. Concretely, the Bernoulli distribution speaks of only two possible outcomes (perhaps with different probabilities), whereas the uniform distribution allows for many outcomes, but they all have the same probability. The case of flipping a fair coin is particularly interesting - it is a Bernoulli event with a uniform distribution.
Hopefully you find this explanation helpful.
A.. The 365 Team