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The biggest problem with Double naught's coin flip example is not its "simplicity". It is the fact that a coin toss is a binomial distribution, not a normal distribution. With a fair coin we know the probability of each possible outcome on each toss is exactly 0.5
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Actually Doc, due to the fact that it is probability, non-normal distributions of flips can and do occur.
Since you want to get real, your FDA example will not tell you one way or the other whether or not YOU will have the reaction/problem to Vioxx. Your event is independent. They are looking at trends, not individual events when it comes to prediction.
The OPer's gunfight will be a mutually exclusive event.