Discrete Mathematics Name: T06 Worksheet Date: Period: 1} In a game, you have a 1143 probability of winning $143 and a 4?.018 probability of losing $10. What is your expected winning? 2) Suppose you buy 1 ticket for $1 out ofa lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What are your expected winnings? 3} Bob and Fred play the following game. Bob rolls a single die. If an even number results, Bob must pay Fred the number of dollars indicated by the number rolled. On the other hand, if an odd number is rolled, Fred must pay Bob the number of dollars indicated by the number rolled. Find Fred's expectation. 4) A contractor is considering a sale that promises a profit of $34,000 with a probability of .7 or a loss (due to bad weather, strikes, and such} of $5000 with a probability of .3. What is the expected profit? 5) Assume that you have a car worth N300 and you wish to insure itfor its full replacement value if it is stolen. If there is a 2% chance that the car will be stolen, what would a fair premium price be? Solve the problem. 6) An insurance company has written 52 policies of $50000, 47? of $25,000, and 918 of $10,000 on people of age 20. If the probability that a person will die at age 20 is 0.0011 how much can the company expect to pay during the year the policies were written? i) A student is taking a standardized test consisting of multiple choice questions for which there are five options for each question. Five points are awarded for each correct answer, but the student loses 2 points for an incurred answer. Questions left blank neither receive nor lose points. Is it in the student's best interest to guess? Solve the problem. 8) Find the expected number of girls in a family of children. 9) Assume that a person spins the pointer and is awarded the amount indicated by the pointer. Determine the person's expectation. Solve the problem. 10} In a raffle, one thousand tickets are sold. There is a grand prize of $6000, a second prize of $400, and a third prize of $100. What ticket price would make this game fair? '11)A certain game involves tossing 3 fair coins. It pays 23 cents for 3 heads,16 cents for 2 heads, and 4 cents for 1 head. What is a fair price to pay to play this game