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1. Two fair dice are thrown and the smallest of the face values, Z say, is...
#1. Two 5-sided fair dice are thrown sequentially, and the face values that come up are recorded. (a) List the sample space. (b) List the elements that make up the following events: A- the sum of the two values is at least 7 B the value of the first die is higher than the value of the second C- the first value is 4 (c) List the elements of the following events: (1) Anc, (2) BuC, (3) An(BuC). (d) Deticenone...
Two roommates, Ken and Billy, play the following game: each throws a pair of fair dice, and the first one to throw a sum of 7 does not have to pay next month's rent (the other roommate has to pay the rent in full: $800). If Ken throws first, the probability that Ken eventually wins—and does not have to pay this month's rent—is 0.55. a. Create a table that shows the probability distribution of Ken's winnings. For a loss, use...
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...
Conditional Expectation A player plays a game. A pair of fair dice is rolled, the outcome of the Red die is denoted by R and the outcome of the Yellow die is deonted by Y. The player does not get to see the outcome of each die but is told the total sum of the two dice, denoted S. She wins W = $10 if the two dice have the same value (like Y = 4, R = 4 or...
2. "Craps" is a game played by rolling two fair dice. To play one round of this game, the player rolls the dice and the outcome is determined by the following rules: If the total number of dots is 7 or 11 (a "natural"), then the player wins. If the total number of dots is 2, 3, or 12 C'craps"), then the player loses. If the total number of dots is 4, 5, 6,8,9, or 10, then this number is...
(15 pts) Determine the missing value(s) that would make the following valid probability distributions. f (x)-a + bx if 0 3 x <6. E(X) 2. Find a and b. (25 pts) Determine the expectation, variance, standard deviation, and cumulative distribution function (c.d.f) for each of the following: A random variable that represents the outcome of rolling two (fair) dice. (10 pts) In a game, a player flips a coin three times. The player wins S3 for every head that turns...
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...
. In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7—that is, 2, 3, 4, 5, or 6. For this bet, the player wins $1 if the result is under 7 and loses $1 if the outcome equals or is greater than 7. Similarly, the player can bet...
(2)(1 pt) In a gambling game a player roles two dice. The player wins as many dollars as the sum of the numbers on the dice (if the dice are a 5 and a 3, then the player wins 8 dollars). Find the expected winnings of this game.
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, using method one, the player can bet $2.00 that the sum will be under 7, that is, 2, 3, 4, 5, or 6. For this bet, the player wins $2.00 if the result is under 7 and loses $2.00 if the outcome equals or is greater than 7. Similarly, using...