Arizona's ‘Cash 4” is a
a. Find the probabilities of winning first prize, second prize, and third prize.
b. Use the results of parts a and the Complement Rule to find the probability of losing.
c. Use the results of parts a and b to find the expected value of Cash 4.
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Chapter 3 Solutions
EBK MATHEMATICS: A PRACTICAL ODYSSEY
- In horse racing, a “trifecta” occurs when a bettor wins by selecting the first three finishers in the exact order (1 St place, 2nd place, and 3rd place). How many different trifectas are possible if there are 14 horses in a race?arrow_forwardIn a competition of 50 professional ballroom dancers, 22 compete in the fox-trot competition, 18 compete in the tango competition. and 6compete in both the fox-trot and tango competitions. How many dancers compete in the foxtrot or tango competitions?arrow_forwardTo raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $8 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $21. If the die shows an even number and the spinner does not show orange, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. $ (c) Is this game fair? Yes Noarrow_forward
- To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $8 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $23. If the die shows an even number and the spinner does not show orange, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) -8 9/32 Yes No (c) Is this game fair? 1 12/32 (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. $2.93 14 Enter a fraction, integer, or exact decimal. Do not approximate. 11/32arrow_forwardSuppose that you and a friend are playing cards and decide to make a bet. If you draw two clubs in succession from a standard deck of 52 cards without replacing the first card, you win $40. Otherwise, you pay your friend $10. If the same bet was made 25 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary. Win: Lose:arrow_forwardThe Knightrola Lottery has been updated to allow choosing 6 numbers out of 63 on a $1 ticket. •Choosing 3 numbers correctly gives a $10 prize. •Choosing 4 numbers correctly gives a $50 prize. •Choosing 5 numbers correctly gives a $5,000 prize. If the Lottery expects to precisely break even, how much is its prize for getting all 6 numbers correct?arrow_forward
- Suppose that you and a friend are playing cards and decide to make a bet. If you draw three twos in succession from a standard deck of 52 cards without replacement, you win $100. Otherwise, you pay your friend $10. If the same bet was made 25 times, how much would you expect to win or lose?arrow_forwardThe most popular game at the Whoville Resort and Casino (WRC) is "Pick Green", which is played with the WRC's Great Urn of Joy. This urn contains thousands of marbles: 85% red and 15% green. The game costs $1 to play and the rules simple: After paying $1, the player repeatedly draws one marble at random, with replacement from the Great Urn of Joy, until they draw a red marble. The player then receives a payoff based on the number of green marbles that they drew, according to the following table: #green marbles 0 1 2 3 4 or more payoff SO $1 $5 $100 $1000 While it is true that Whos don't earn extra cash for drawing more than 4 green marbles, they do get a certificate listing their total, and these certificates are a source of great pride in Whoville. What is the probability that a player receives (exactly) $5 in this game? What is the probability that a player receives at least $1 in this game? Consider the WRC's point of view: their profit-per-game is $1 - payoff. What is the expected…arrow_forwardThe trifecta at most racetracks consists of selecting the first-, second-, and third-place finishers in a particular race in their proper order. If there are six entries in the trifecta race, how many tickets must you purchase to guarantee a win?arrow_forward
- In a lottery, there 250 prizes of $5, 50 prizes of $25, and ten prizes of $100. Assuming that 10,000 tickets are to be issued and sold, what is a fair price to charge to break even? (Enter your answer to the nearest cent)arrow_forwardSuppose that you and a friend are playing cards and decide to make a bet. If you draw two face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards without replacing the first card, you win $40. Otherwise, you pay your friend $10. If the same bet was made 25 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary. Answer E Keypad Keyboard Shortcuts O Win O Losearrow_forwardA buyer paid $41,400,including the buyer's premium, for a car auction. If the auction adds a 15% buyer's premium to the sale price of the car, then what was the sale price of the car? The sale price of the car was $.....(Type an integer or a decimal.)arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL