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1. In a certain country, approximately 1 out of 2100 people have a certain characteristic. What is the probability that in a town of 3000 people, at least one person has that characteristic? 2. Suppose that the profit made on the sale of a necklace can be either $7, $9, $11, $13, $1 5, or $17 . with respective probabilities 1/12, 1/12, 1/4 ,1/4, 1/6, and 1/6. What is the expected value of the profit here? 3. A coin is biased so that a head is three times as likely to occur as a tail. Find the expected number of tails when the coin is tossed twice. 4. In a gambling game a woman is paid $3 if she draws a Jack or a Queen and $5 if she draws a King or an Ace from an ordinary deck of 52 cards. If she draws any other card she does not win anything. How much should the woman pay to play the game if the game is to be a \"fair\" game? (A \"fair\" game is defined as a game with Expected Value = 0.) 5. Five percent of the disk controllers produced by a plant are known to be defective. A sample of fifteen controllers is drawn randomly from each month's very large production run and the number of defectives noted. What proportion of these monthly samples would have at least two defective controllers? (Hint: the proportion of the monthly samples with at least two defective controllers is the same thing as the probability that a particular month's sample has at least two defective controllers .....from the definition of probability as the long-run preportion of the time that an event occurs)