Suppose you flip a fair coin repeatedly. For each i $=1,2,...,$ let Ai be the event that flip #i and flip #i $+1$ are both Heads. For example if your first four flips are TIGHT, then A$1$ has not occurred, A$2$ has occurred, and A$3$ has not occurred $($and we don$$t know yet about A$4,$ A$5,...).$