Math 142 – October 11, 2011 Name: Leave your answers as fractions. Unreduced is okay. 1. Two candidates, Smith and Wilson, are running for mayor. The voting breakdown is shown below in the table: Rep (R) Dem (D) Indep (I) Total Smith (S) 72 38 15 125 Wilson (W) 46 61 22 129 Total 118 99 37 254 A voter is selected at random. Determine these probabilities: a) The probability the voter voted for Smith, given the voter was Republican. ( |):_________ b) The probability the voter was Independent, given the voter voted for Wilson. (|)_________ c) Determine (|): _________ d) Determine ( | ∪ ): _________ 2. A jar has 15 red, 20 orange and 22 blue candies. Two candies are drawn without replacement. Find these probabilities: a) The second candy is blue given the first was red. _________ b) The second is orange given the first was blue. _________ c) Both candies were blue. _________ d) (2 pts extra credit) Both candies are of different color. _________ 3. Tourists to Las Vegas are surveyed. 52% visit Hoover Dam, 31% visit the Strip, and 14% visit both the Strip and Hoover Dam. Determine the following probabilities. You may leave your answer in decimal format. Hint: draw a Venn. a) The probability a tourist visited the Hoover Dam given the tourist visited the Strip. _________ b) The probability a tourist visited Strip given the tourist visited Hoover Dam. _________ c) The probability a tourist did not visit Hoover Dam given the tourist did not visit the Strip. _____4. You roll a single die once. If it lands a 6, you get $10. Otherwise, you get nothing. The cost to play is free. What is the expected value of one roll of this die? 5. A bag has 20 tokens in it. They all feel the same. One is gold colored and worth $20. Two are silver colored and worth $5 each. The other 17 are worth nothing. For $3, you can reach in and randomly grab one token. What is the expected value of this “game”? 6. A lottery sells 100 tickets for $1 each. One ticket is the winner, with a jackpot of $75. The rest are worthless, and you lose your $1. Your friend’s bright idea is to buy all the tickets. Use Expected Value to explain why this is a lousy idea. Show your calculation and give a one sentence explanation. 7. A roulette wheel has 38 slots. The cost to play is $1. If the ball lands in a slot you picked, you win $36. Otherwise, you lose the $1. a) Find the Expected Value of one play. _________. Is this game in your favor? (Y/N)______ b) If you played 100 games, how much up or down can you expect to be? _________ c) What is the fair price to play this game?
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