Analyzing the Outcomes of Games

D Game 1: Coin Flip Use this game for questions 1-3. For this game, you must flip a coin 4 times in a row and observe the number of heads. The cost to play is $10. The payouts are given below: Event: Number of Heads Payouts 0 $20 $10 2 $8 $10 $20 D Question 1 5 pts Game 1: Coin Flip Complete the following probability distribution table. For probability, express your answer as a simplified fraction. Event: Number of Heads Number of Ways Probability Payouts 0 $20 1 $10 2 $8 3 $10 4 $20 D Question 2 5 pts Game 1: Coin Flip Which of the following is the expected value of the game to the player. -$0.50 -$1.50 $1.50 $0.50 D Question 3 3 pts Game 1: Coin Flip Which of the following is the correct probability distribution of the coin flip game? 4 FlipD Question 3 3 pts Game 1: Coin Flip Which of the following is the correct probability distribution of the coin flip game? 4 Flips as 1 Number of Heads 2 Number of Heads " Series 1 4 Flips ass 1 Number of Heads 2 Number of He 3 Number of Heads Series 1 4 Flips 1 Number of Heads Series 1 4 Flips 125 Number of Heads 1 Number of Heads 2 Number of Heads 3 Member of Heads 4 Number 4 Fups Frequency 0 Number of Heads 1 Number of Heads 2 Number of Heads 3 Number of Heads Series 1Game 2: Dice Roll Use this game for questions 4-6. For this game, you must roll two dice at the same time and observe the sum of the pips on top. The cost to play the game is $12. The payouts are given below: Event: Dice Roll Sum Payouts $72 $36 $18 6 0 7 8 10 $18 11 $36 D Question 4 10 pts Game 2: Dice Roll Complete the following probability distribution table. For probability, express your answer as a simplified fraction. Event: Dice Roll Sum Number of Ways Probability Payouts $72 3 $36 $18 $9 0 00 V a U 0 $9 10 $18 $36 $72 D Question 5 5 pts Game 2: Dice Roll Which of the following is the expecte value of the game to the player? (Remember that it costs $12 to play) $1.00 $4.50 $0.50 $13.00 D Question 6 6 pts Game 2: Dice RollQuestion 6 6 pts Game 2: Dice Roll Which of the following adjustments to the game would make the game fair? Select all that apply. Increase the cost to play by $1 Remove the payout for rolling a 5 Remove the payout for rolling a Decrease the cost to play by $2 Include a payout of $6 for rolling a 7 Game 3: Drawing a Card Use this game for questions 7-9 For this game, you must draw a card from a standard 52-card deck. If you draw an Ace, you win $20.00. If you draw a face card, you win $5.00. If you draw any other card, you lose $4.00. Question 7 6 pts Game 3: Drawing a Card Fill in the probability of each event given in the table below. Enter your answer as a simplified fraction. Event Probability Drawing an Ace in a standard 52- card deck Drawing a face card (King or Queen or Jack) in a standard 52-card deck Drawing any other card (2, 3, 4, 5, 6, 7, 8, 9, or 10) in a standard 52 card deck Question 8 5 pts Game 3: Drawing a Card Calculate the expected value of the game. Hint: Use the probability table above. Round the expected value to the nearest cent. The expected value is $ D Question 9 5 pts Game 3: Drawing a Card One ace is removed from the deck. Calculate the expected value of the game with one ace removed. The game is now as follows: For this game, you must draw a card from a standard 52-card deck, with one ace removed. If you draw an Ace, you win $20.00. If you draw a face card, you win $5.00. If you draw any other card, you lo Hint: Calculate the probability of the following with one ace removed from the deck. 1. Drawing an ace 2. Drawing a face card 3. Drawing any other card Round the expected value to the nearest cent. The expected value with one ace removed is $