180ahw3 - MATH 180A Introduction to Probability Homework...

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MATH 180A – Introduction to Probability Homework 3 (due 10/25/06) 1. On a multiple-choice quiz with 3 possible answers for each of the 10 questions, what is the expected number of correct answers a student would get just by guessing? 2. Two marbles are drawn without replacement from a box that contains 5 red and 5 blue marbles. If they match, you win $1.10; otherwise, you lose $1.00. Calculate the expected value and the standard deviation of the amount you win. 3. Jim and Sara play Rock, Paper, Scissors – read rules here . Assume that each round both Jim and Sara choose among rock, paper and scissor with equal probability. (a) What are the chances that the game ends on the sixth round? (b) What are the chances that Sara wins on the fourth round? (c) Suppose Jim and Sara play the game 10 times. Compute the expected number of times that at least three rounds are needed to settle the game. 4. A newsboy purchases daily news papers at 10 cents and sells them at 15 cents. However,
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Unformatted text preview: he is not allowed to return unsold papers. He has 20 customers and each customer buys his paper with probability 1/3. Suppose the newsboy buys 20 papers every day. What is the probability that he makes a profit at least 6 days in a given week? *Bonus* Suppose the newsboy buys m papers every day. What value of m makes maximizes his daily expected profit? 5. A father buys lottery tickets to get a doll for his daughter. Assuming that each lottery ticket wins a doll with probability 1/100, approximate the number of tickets the father needs to buy in order to have a 95% chance of winning at least 1 doll. *Bonus* Another father does the same to get a doll for each one of his three daughters. Approximate the number of tickets the father needs to buy in order to have a 95% chance of winning at least 3 dolls....
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