Most of the main ideas about probability come up right at the beginning. Two major ones are independence and randomness . Even more important for clear thinking is the notion of a probability model . ROULETTE A gambler is betting on what he thinks is a fair roulette wheel. The wheel is divided into 38 segments, of which: ▪ 18 segments are black. ▪ 18 segments are red. ▪ 2 segments are green, and marked with zeroes. If you bet $10 on red, and the wheel stops at red, you win $20. Likewise if you bet $10 on black and it stops at black, you win $20. Otherwise you lose. The house always wins when the wheel stops at zero. Now imagine that there has been a long run–a dozen spins–in which the wheel stopped at black. The gambler decides to bet on red, because he thinks: The wheel must come up red soon. This wheel is fair, so it stops on red as often as it stops on black. Since it has not stopped on red recently, it must stop there soon. I'll bet on red. The argument is a risky one. The conclusion is, “The wheel must stop on red in the next few spins.” The argument leads to a risky decision. The gambler decides to bet on red. There you have it, an argument and a decision. Do you agree with the gambler?