ࡱ> `b_% bjbj%% ".GGl666J J"&' ' ' 5"7"7"7"7"7"7"$$ &r["6' @' ' ' [" &p" ' R6&5" ' 5" ^ %R "6!"& /mJ !!""0"!f' '!" JJGroup Name: Names of Group Members: ________________________ ________________________ ________________________ ________________________ ________________________ These probability problems require some creative thinking. For a few of these problems, it may be helpful to try trial-and-error first. Use common sense, and dont be afraid to think outside the box! Problems: Work with your group to use your math skills to solve these problems. They are arranged in increasing order of difficulty. Dont worry if you cant solve all of them immediately, especially the bonus questions. The Cartidas family has several children. 5 of them play football, 4 of them play hockey, and 3 of them play tennis. Each child plays only 2 sports. What is the smallest number of children they could have? You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls. He then says, "Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die." How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble? A gambler goes to bet. The dealer has 3 dice, which are fair, meaning that the chance that each face shows up is exactly 1/6. The dealer says:"You can choose your bet on a number, any number from 1 to 6. Then I'll roll the 3 dice. If none show the number you bet, you'll lose $1. If one shows the number you bet, you'll win $1. If two or three dice show the number you bet, you'll win $3 or $5, respectively." Is it a fair game? A swindler once approached an honest man with a die. He handed him the die and told him about the bet. The die had six sides. If the man rolled a ONE, he wins, and gets back twice the amount of his bet. If not, the swindler would keep the bet. "But...my chances are only one out of six," retorted the man. "True," grinned the swindler, "But I'll give you three tries to get a one." The man considered. Three tries, with each try having a 1/6 chance of winning. So his chances of winning is 1/2. Why not give it a try? Is the bet really fair? If not, what are the chances of the man winning? Henry has been caught stealing cattle, and is brought in to town for justice. The judge is his ex-wife Gretchen, who wants to show him some sympathy, but the law clearly calls for two shots to be taken at Henry from close range. To make things a little better for Henry, Gretchen tells him she will place two bullets into a six-chambered revolver in successive order. She will spin the chamber, close it, and take one shot. If Henry is still alive, she will then either take another shot, or spin the chamber again before shooting. Henry is a bit incredulous that his own ex-wife would carry out the punishment, and a bit sad that she was always such a rule follower. He steels himself as Gretchen loads the chambers, spins the revolver, and pulls the trigger. Whew! It was blank. Then Gretchen asks, "Do you want me to pull the trigger again, or should I spin the chamber a second time before pulling the trigger?" What should Henry choose? Mismatched Joe is in a pitch dark room selecting socks from his drawer. He has only six socks in his drawer, a mixture of black and white. If he chooses two socks, the chances that he draws out a white pair is 2/3. What are the chances that he draws out a black pair? 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