D E Canvas.c0|orado.Edu C 3.31 Hearts win. In a new card game, you start with a well-shufed i'ull deck and draw 3 cards without replacement. If you draw 3 hearts, you win $50. if you draw 3 black cards, you win $25. For any other draws, you win nothing. (a) Create a probability model for the amount you win at this game. and nd the expected winnings. Also compute the standard deviation of this distribution. (b) If the game costs $5 to play, what would be the expected value and standard deviation of the net prot (or loss)? (Hint: prot = winnings 7 cost; X 7 5) (c) If the game costs $5 to play, should you play this game? Explain. 3.32 Is it worth it? Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card ( jack, queen or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs. (3) Create a probability model and nd Andy's expected prot per game. (b) Would you recommend this game to Andy as a good way to make money? Explain. 3.33 Portfolio return. A portfolio's value increases by 18% during a nancial boom and by 9% during normal times. It decreases by 12% during a recession. What is the expected return on this portfolio if each scenario is equally likely? 3.34 Baggage fees. An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have one piece of checked luggage and 12% have two pieces. We suppose a negligible portion of people check more than two bags. (a) Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation. (b) About how much revenue Should the airline expect for a ight of 120 passengers? With what standard deviation? Note any assumptions you make and if you think they are justied. 3.35 American roulette. The game of American roulette involves spinning a wheel with 38 Slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money. Suppose you bet $1 on red. What's the expected value and standard deviation of your winnings