Suppose it is possible for a coin to land on its edge. A valid probability model should account for this outcome. If we assume that the coin is
equally likely to land heads or tails, explain why the probability for
heads (or tails) cannot be 1/2 when it is possible for the coin to land
on its edge.__________________________________________________________
Well, if we consider it from the aspect of the Law of Total Probability, then the answer becomes clear!
The Law of Total Probability states that the sum of all the possible probabilities must equal 1. Hence:
Therefore, if P(heads) and P(tails) both equal 0.5, then it becomes obvious what’s wrong here:
But, we are told it’s possible for the coin to land on its edge- whereas our Law of Total Probability is saying it isn’t!