In a gambling game, a player is paid Php 100 if he draws a jack or a queen and Php 200 if he draws a king from an ordinary deck of 52 playing cards. If draws any other card, he losses. How much should he pay to play if the game is fair?
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- A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 15 spots labeled $1, 9 spots labeled $2, and 9 spots labeled $10, how much should a player expect to win on average?A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 8 spots labeled $1, 16 spots labeled $2, and 1 spots labeled $10, how much should a player expect to win on average?An urn contains 25 balls, 40% of which aregreen. A contestant reaches in the urn tochoose three balls; the contestant will win$200 if he or she selects a green ball, butwill lose $120 for any other colour. Is eachversion of the game a fair game? Justifyyour response.
- James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel. -if the ball lands in a red space, he wins $25 on his 'red' but loses $5 on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000 let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23 u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053 FILL IN THE BLANK if you play 2500 times, and Let, x (x bar)= the mean winnings (or…You have been asked to play a card game. A card is dealt from a complete deck offifty-two cards (no jokers). A deck has 4 aces, 4 kings, 4 queens, 4 jacks, and 36 other cards.It works like this:• If the card is a ace, you lose $4.• If the card is a king or jack, you lose $10.• If the card is a queen, you win $8.• If the card is anything else, you win $1.Find the expected value of the game. Write the excepted value rounded to the nearest centAt your local carnival, there is a game where 40 rubber duckies are floating in a kiddie tub, and they each have their bottoms painted one of three colors. 55 are painted pink, 16 are painted blue, and 19 are painted purple. If the player selects a duck with a pink bottom, they receive three pieces of candy. If they select blue, they receive two pieces of candy. And if they select purple, they receive one piece of candy. If the game is played 42 times, what are the minimum and maximum amounts of candy that could be handed out?
- A bag contains 16 red coins, 8 blue coins, and 8 green coins. A player wins by pulling a red coin from the bag. Is this game fair?If a person rolls doubles when tossing two dice, the roller profits $ 65 , that is, the roller receives $ 65 more than the cost of the game. If the game is fair, how much should the person pay to play the game?The player pays a fee of $5 to play. The player then rolls a 12-sided die three times. If the player rolls a 7 on any of the three rolls, they win a prize. The prize is determined by the number of 7s rolled. If the player rolls one 7, they win $5. If the player rolls two 7s, they win a $10. If the player rolls three 7s, they win $20. Compare the theoretical results of the game to the experimental results, including a discussion of whether the results were typical or rare. Theoretical results: Roll (including all 3 rolls) Result Money earned 1 7,7,7 $15 2 2,4,5 $5 3 5,7,9 $5 4 1,9,3 $0 5 2,12,7 $5 6 3,12,3 $0 7 7,4,8 $5 8 6,7,7 $10 9 5,12,4 $0 10 7,5,7 $10 Experimental results: Roll (including all 3 rolls) Result Money earned 1 1,3,7 $5 2 3,6,4 $0 3 7,6,9 $5 4 8,7,7 $10 5 11,4,1 $0 6 6,5,7 $7 7 4,6,3 $0 8 7,1,9 $7 9…