

Therefore, the minimum amount needs to be at least $3.33, so that casino will not be in loss.
What is the expectation (or expected value) of the following: Consider a casino game where the...
2. (25 points) Sekora International Casino (SIC) is launching a new game making use of fair 6-sided dice . In phase 1, roll two 6-sided dice and compute the difference between the rolls. Call this difference . In phase 2, roll r dice, and add up the total of the rolls. This is the payout in dollars of the game. (with the numbers 1-6 on the sides). The game proceeds in two phases as follows: (a) (5 points) In the...
Chris is playing a dice game at a casino. The game is played by rolling a single six-sided dice. If an even number shows up, the player wins 10 times whatever shows up (for example, if 4 shows up, then he wins 4 x10 = $40). If an odd number shows up, the player loses $25. a. (3 pts) What values does X take on? X P(x) a. b. c. (4 pts) Write out the probability distribution of X in...
Consider a play of the casino game `Quick Draw'. In this game, a player pays $11 to play. The player picks one card from a standard pack of 52 cards (i.e. there are four A’s and four K’s in a standard pack of 52 cards). If the player gets an Ace, they win $50 but loose the amount they paid to play (the profit is revenue minus cost); if the player selects a King, they win $30 but loose the...
A person must pay $ $ 8 to play a certain game at the casino. Each player has a probability of 0.21 of winning $ $ 14, for a net gain of $ $ 6 (the net gain is the amount won 14 minus the cost of playing 8). Each player has a probability of 0.79 of losing the game, for a net loss of $ $ 8 (the net loss is simply the cost of playing since nothing else...
At Quark’s casino, there is a game called “High Five”, where you paid $1 to roll a fair die once. If a 5 shows up, you get back $5, nothing otherwise. (a) Let X be the amount of money you WIN by playing this game. Fill in the details in the table below. x p (X) = x (b) Calculate E(X), the expected amount of money you win by playing this game. (c) Is the outcome of this game favorable...
4. [6 marks] Consider a play of the casino game 'Quick Draw'. In this game, the player pays $10 to play. He/she picks onē card from the standard deck of 52 cards (i.e. four A's, four K's, etc.). If the player selects an "A", he/she wins $50 (i.e. the profit is $40); if the player selects a "K", he/she wins $30 (i.e. the profit is $20). Otherwise, the player wins nothing and also loses the bet of $10. Let the...
A person must pay $ 5 to play a certain game at the casino. Each player has a probability of 0.15 of winning $ 13, for a net gain of $ 8 (the net gain is the amount won 13 minus the cost of playing 5). Each player has a probability of 0.85 of losing the game, for a net loss of $ 5 (the net loss is simply the cost of playing since nothing else is lost). What is...
A dice game is played with two distinct 12 sided dice. It costs $3 to roll the pair of dice one time. The payout scheme is as follows 1. Sum of 13 pays $10 Sum of 11 or 15 pays $6 Sum of 7, 9, 17, or 19 pays $3 Any other roll doesn't pay. What is the expected gain/loss after playing the game one time? A "fair" game is one in which the expected gain/loss after playing once is...
15. Your friend challenges you to a game. She says that she is going to roll 2 6-sided dice. If the first die rolls at least 5, you win if the second die rolls less than 5. If the first die rolls less than 5, you win if the second die rolls at least 5. This seems fair. Is it? (a) What is the probability that you win this game? To incentivize you, your friend says that she will pay...
In the game of Lucky Sevens, the player rolls a pair of dice. If the dots add up to 7, the player wins $4; otherwise, the player loses $1. Suppose that, to entice the gullible, a casino tells players that there are many ways to win: (1, 6), (2, 5), and soon. A little mathematical analysis reveals that there are not enough ways to win to make the game worthwhile; however, because many people's eyes glaze over at the first...