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If you did the Probably? activity and haven't done Square Scoops, why don't you give it a try now? You're going to see some similarities between permutations, tree diagrams, and probability.
Although there was some work on the chance involved in dice games beginning in the late 1400s, probability theory didn't appear until the mid 1600s. The first discussions were about designing rules for games of chance. Now probability is important in almost everything we do. What is the chance that it will rain on the day of the big game? What are the odds that you will get the flu if you get a flu shot? Is it more likely that you'll get hit by lightning or win the lottery? (Getting hit by lightning: about 100 people per year get hit by lightning in the U.S. and there are about 290 million people in the U.S. That means the odds of getting hit are about 1 in 3 million. The odds of choosing six numbers out of fifty-one is about 1 in 18 million.)
Did you notice that a tree diagram (check out the Back Story on Square Scoops) looks a little like what we did to figure out the probabilities? What if we put a green, red, and blue tile in a bag and wanted to know the chance of pulling out a green tile first, the red tile second, and the blue tile third? You can look at the tree diagram from Square Scoops and figure out that there are six ways of pulling the tiles out and only one of them is the order we're interested in. That means that the chance of pulling the green-red-blue tiles in that order is one in six.

copyright 2003, Center for Hands-On Learning