In a dice game, the player independently rolls a fair red die and a fair green die.The
player wins if and only if the red die shows a 1, or 2, or 3, or if the total on the two
dice is 11. What is the probability the player will win?
In a dice game, the player independently rolls a fair red die and a fair green...
In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is 16
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...
3. Consider independently rolling two fair dice, one red and the other green. Let A be the event that the red die gets a 3, B be the event that the green die gets a 4, and C be the event that the total number showing on the two dice is 7. A. Are A and B independent? Explain. B. Are B and C independent? Explain.
Bob and Doug are playing the following game. Bob starts by rolling two fair dice; if the sum of his dice is six, then he wins the game. If not, then Doug rolls the dice, and if the sum of his rolls is seven, then he wins the game. If neither player wins the game during the first round, then they repeat the process (with Bob going first) until someone wins a round. What is the probability that Bob wins...
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...
In a dice game, you roll a fair die three times, independently. If you don’t roll any sixes, you lose 1 dollar. If you roll a six exactly once, you win one dollar. If you roll a six exactly twice, you win two dollars. If you roll a six all three times, you win k dollars. (A) Let k = 3. What is the expected value of the amount you would win by playing this game (rounded to the nearest...
In a casino game, the player rolls a pair of dice. If the first throw is a 7 or an 11, the player wins automatically. What is the probability that the player will win on the first throw? 30A. 30B. In 1999, the stock market took big swings up and down. A survey of 997 investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an investor tracked their portfolio daily...
If we roll a red 6-sided die and a green 6-sided die (both are fair dice with the numbers 1-6 equally likely to be rolled), what is the probability that we get (i) A 5 on the green die AND a 3 on the red die? (ii) A 5 on the green die OR a 3 on the red die? (iii) A 5 on the green die GIVEN we rolled a 3 on the red die?
Example Consider the following dice game. A pair of standard ( fair ) dice are repeatedly rolled. If a ’ 7 ’ comes up before an ’ 11 ’ , then the player wins, otherwise the player loses. Let W be the event that the player wins. Find P(W). To say the dice are fair is equivalent to assuming that Laplace’s rule holds and the 36 possible outcomes for a throw of the dice are equally likely. For convenience, an...
1) You roll 2 fair dice, a green one and a red one. a. What is P(a 1 on green die and a three on red die)? b. What is P((one on green die and three on red die) or (three on green die and one on red die))? c. What is the probability of getting a sum of 11?