Johnny Mathis sang "Chances Are", but he wasn't crooning about luck so much as love. In math and science, chance can more accurately be expressed and measured using the language of probability. For instance, we know that if a person flips a coin, there's a .5 (or 50 percent) probability that it will land showing heads, and an equal probability it will show tails. -- unless the coin flipper is using a two-headed coin.
Probability becomes confusing for folks when presented with a slightly more involved problem. Let's say the same person intends to flip a coin 100 times. Other things being equal, there is a reasonable probability that approximately 50 of those flips will show heads, and 50 tails. So let's say we've arrived at the halfway point with 45 heads and 5 tails. Shouldn't the probability be greatly increased that the next toss will be tails? Alas, no. For you see, each toss is a discreet event, and that is what the probability is based on. The next toss still has a 50 percent probability of being either heads or tails.
Ah, so what if we have 100 people, all tossing a coin at the same time? The same odds hold true for each individual. For the group as a whole, it is reasonable to expect that approximately half will be heads, and half tails.
Things really get dicey (as it were) when we introduce conditional probability, which is the interaction of not one variable (heads or tails), but two variables which may affect each other. Steven Strogatz, a math professor who teaches conditional probability, has broken it all down nicely for us in his article on the interaction of variable outcomes. The subject is a bit tricky, but well worth understanding, since we encounter conditional probability every day of our lives. Check it out.
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