math 218 fall 2003 final

math 218 fall 2003 final - MATH 218 FINAL EXAMINATION...

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MATH 218 FINAL EXAMINATION December 17, 2003 Professors: J. Colwell, F. Lin, K. Styrkas, E. Verona, Z. Vorel. Problem 1. A random sample of 50 purchases at a department store produced the follow- ing contingency table for the method of payment and the size of the purchase: Cash Credit card Debit card Under $30 5 2 2 $30 to $100 2 10 9 Over $100 1 12 7 (a) Given that a purchase was made with a debit card, find the probability that it was at least $30. (b) Given that a credit card purchase was at least $30, find the probability that it was over $100. (c) Find the probability that a purchase was under $30. (d) Find the probability that a purchase was paid by cash. (e) Are “Under $30” and “Cash” independent events? Explain. Problem 2. A carnival has three games. In Game A, the player has a 4% chance of winning. In Game B, the player has a 3% chance, and in Game C, a 2% chance. You know that your friend, who likes the carnival, is equally likely to play any of the three games. (a) Draw a tree diagram to depict this situation. Include all events and probabilities (conditional and joint) involved. (b) You go to the carnival and see your friend with a stuffed dragon which she won at one of the games. What is the probability that she won it at Game A? (c) Inspired by your friend’s success, you decide to play one game. Unfortunately, Game A has ceased to operate for the day. In order to decide whether to play Game B or Game C, you first flip a fair coin. What is the probability that you win a game?
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