Let’s play a game! It costs you only $10 to play! Roll two dice. If you...

Let’s play a game! It costs you only $10 to play! Roll two dice. If you roll snake eyes (two 1’s), then I’ll give you $500. If you roll anything else, then I’ll give you nothing. Using expected value, decide if you should play this game!

Expert Solution

orchestra answered 1 year ago

Two players A and B play a game of dice . They roll a pair of...

Two players A and B play a game of dice . They roll a pair of dice alternately . The player who rolls 7 first wins . If A starts then find the probability of B winning the game ?

This problem concerns the dice game craps. On the first roll of two dice, you win...

This problem concerns the dice game craps. On the first roll of two dice, you win instantly with a sum of 7 or 11 and lose instantly with a roll of 2,3, or 12. If you roll another sum, say 5, then you continue to roll until you either roll a 5 again (win) or roll a 7 (lose). How do you solve for the probability of winning?

In the game of Craps, you roll two dice. When you bet on a “snake eyes”,...

In the game of Craps, you roll two dice. When you bet on a “snake eyes”, meaning a 1 on both dice, you win $30 for each $1 you bet. Otherwise, you lose your dollar. What is the probability of winning this bet? What is the expected value of making this bet? If you play this game 100 times, how much would you expect to lose?

You make a carnival game, where the player rolls two fair dice (in a single roll)...

You make a carnival game, where the player rolls two fair dice (in a single roll) and attempts to roll doubles (meaning both dice show the same number). The player puts down a dollar to play the game. If the player loses, they lose their dollar. If the player wins, they win $3 (and do not lose their original dollar). Answer the following (5 pts total). If you are running the game, what is the expected value of how much...

We will simulate a dice game in which 2 dice are thrown. If the roll is...

We will simulate a dice game in which 2 dice are thrown. If the roll is 7 or 11, you win. If the roll is 2, 3, or 12, you lose If the roll is any other value, it establishes a point. If with a point established, that point is rolled again before a 7, you win. If, with a point established, a 7 is rolled before the point is rolled again you lose. Build your algorithm incrementally. First write...

suppose you roll two fair dice. A) what is the probability that you will roll an...

suppose you roll two fair dice. A) what is the probability that you will roll an even number on the first die AND a 5 on the second die B) What is the probability that the sum of the numbers on the two dice is 9? show all work.

Two players A and B play a dice game with a 6-face fair dice. Player A...

Two players A and B play a dice game with a 6-face fair dice. Player A is only allowed to roll the dice once. Player B is allowed to roll the dice maximally twice (that is, Player B can decide whether or not she or he would roll the dice again after seeing the value of the first roll). If the player with the larger final value of the dice wins, what is the maximal probability for Player B to...

You roll two fair dice. Let A be the event that the sum of the dice...

You roll two fair dice. Let A be the event that the sum of the dice is an even number. Let B be the event that the two results are different. (a) Given B has occurred, what is the probability A has also occurred? (b) Given A has occurred, what is the probability B has also occurred? (c) What is the probability of getting a sum of 9? (d) Given that the sum of the pair of dice is 9...

Let’s suppose that you are going to play the lottery game Powerball. To play, you pick...

Let’s suppose that you are going to play the lottery game Powerball. To play, you pick five different numbers from 1 through 69 plus one Powerball number from 1 through 26. Which is a more likely combination of winning numbers: 1, 2, 3, 4, 5, 6 or 7, 21, 25, 32, 40, 56? Explain your answer. For a $500,000,000 jackpot, which of the two combinations would likely be more lucrative for you if it were to win? In other words,...

You pay $1 to play a game. The game consists of rolling a pair of dice....

You pay $1 to play a game. The game consists of rolling a pair of dice. If you observe a sum of 7 or 11 you receive $4. If not, you receive nothing. Compute the expected value and standard deviation for this game?

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