[QUOTE]Should you walk outside of your house at night without first turning on the lights and looking out the window? Even though there has been no incident after several years doesnt mean it will never happen. In fact, after a series of no incidents tells me that it might be just about to happen... [QUOTE]
Um, no. Not unless you are talking about mutually inclusive events, which I don't believe you are.
For example, based on statistics of the sun coming up every day for the past 1460000000000 days (4 billion years of days), I can postulate that the sun will come up every day forever and have a very high statisticaly probability that this will in fact happen. This would be a misapplication of statistics because each day's event of rise isn't mutually exclusive from the past events.
You see, we know that the sun won't last for ever and does have a finite life as a star. So with every day that passes, there is a greater and greater chance that the sun will die and hence not "come up." In other words, each day's event is tied to the events of the past. They are mutually inclusive.
Take the example with tossing a coin and doing heads or tails where it is assumed that the coin is actually (truly) balanced and 'sides' or 'edges' are not a realistic option. Each toss results in a 50% chance of a given outcome. Now say that you had 9 results that were actually the same, say they were all heads. What is the chance the 10th toss will result in heads? It can be argued with statistics that the chances are very good given the 9 previous outcomes. It can be argued with statistics that the chance is very bad as the longer you continue with such a pattern of results, the more likely the pattern is to be broken. Both sets of analysis would in error because they are treating the events as being mutually inclusive.
In reality, the chance of that 10th toss being heads again is the exact same as the original toss, 50-50. That is because each toss is mutually exclusive.
Applying such statistics to human behavior is problematic for this reason. People love to use statistics for things like estimating how much ammo they will need in a gun fight. While it may be most common for folks to only need 2-3 rounds for a gun fight (mean, median, or mode), what has happened in past gun fights does not determine or give a percentage indication of what will happen in any new gun fight in which any of us participate.
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In fact, after a series of no incidents tells me that it might be just about to happen...
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No. Note statistically, not unless you are doing something to influence that outcome. Mutually exclusive events are not linked through time (hence part of the reason they are mutually exclusive). There is no more chance of you having an event happen today than yesterday simply because of the passage of time just like there is no more chance of me winning the lottery today because I haven't won't it in the past 10 years of paying.