Question

In: Statistics and Probability

A new casino game involves rolling 3 dice. The winnings are directly proportional to the total...

A new casino game involves rolling 3 dice. The winnings are directly proportional to the total number of sixes rolled. Suppose a gambler brings his own dice and plays the game 100 times, with the following observed results (number of sixes, number of rolls): (0, 48), (1, 35), (2, 15), (3, 3). The casino becomes suspicious of the gambler and asks you to determine whether the dice are fair. If the dice are fair, you would expect the probability of rolling a 6 on any given toss to be 1/6. Assuming that the number of sixes in the three rolls are independent, the number of sixes in three rolls should follow a Binomial Distribution with n=3 and p=1/6. Using a level of significance of 0.01, what is the critical statistical value to determine whether or not the binomial distribution is a good fit for this data? Report answer to 3 significant figures.

Solutions

Expert Solution

orchestra answered 1 year ago
Next > < Previous

Related Solutions

A new casino game involves rolling 3 dice. The winnings are directly proportional to the total...
A new casino game involves rolling 3 dice. The winnings are directly proportional to the total number of sixes rolled. Suppose a gambler brings his own dice and plays the game 100 times, with the following observed results (number of sixes, number of rolls): (0, 48), (1, 35), (2, 15), (3, 3). The casino becomes suspicious of the gambler and asks you to determine whether the dice are fair. If the dice are fair, you would expect the probability of...
A new casino game involves rolling 2 dice. The winnings are directly proportional to the total...
A new casino game involves rolling 2 dice. The winnings are directly proportional to the total number of sixes rolled. Suppose a gambler plays the game 100 times, with 0,1 and 2 sixes observed 40, 30, 30 times respectively. Do you reject the hypothesis H0: that the dice are fair at 5% level of significance? Use the fact that P(χ2^2>5.99) = 0.05.
A new casino game involves rolling a die. The winnings are directly proportional to the result...
A new casino game involves rolling a die. The winnings are directly proportional to the result of the number rolled. Suppose a gambler plays the game 108 times, with the following observed counts: Observed Number, Observed Frequencies 1 6 2 12 3 24 4 27 5 9 6 30 The casino becomes suspicious of the gambler and wishes to determine whether the die is fair. What would you conclude at = 0:05? Is the test you adopt an exact test...
Roulette is a casino game that involves spinning a ball on a wheel that is marked...
Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1-36 are red and half are black, 0 and 00 are green. Each number occurs only once on the wheel. The most common bets are to bet on a single number or to bet on a color (red or black). The pocket in which the ball lands on the wheel determines...
Roulette is a casino game that involves spinning a ball on a wheel that is marked...
Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black or green. Half of the numbers 1-36 are colored red and half are black. The numbers 0 and 00 are green. Each number occurs only once on the wheel. We can make many different types of bets but the simplest are to bet on a number or on a color (either red or black). These are the...
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?
You and a friend are rolling a set of 8 dice. The game works such that...
You and a friend are rolling a set of 8 dice. The game works such that if a die shows the values 1, 2, 3, or 4 you will get a point for that die. Each die that shows 5 or 6 your friend will get a point for. Construct a probability model for a single roll of the dice then answer the following. Step 2 of 5: What is the probability that your friend will score 2 points? Step...
A casino introduces a new game. In this game you roll a die and the upper...
A casino introduces a new game. In this game you roll a die and the upper most number is recorded. If you roll an odd you lose. If you roll a 2 you win $1, if you roll a 4 you win $5 and if you roll a 6 you win $10. A) If the game costs $5 to play what is the expected gain/loss of the game? B) Instead of $5 to play, what should the cost to play...
1.) In rolling a pair of dice, what is the probability of a total of 4...
1.) In rolling a pair of dice, what is the probability of a total of 4 or less? 2.) A blue die and a red die are tossed together. Find the probability that the sum is less than 7, given that the blue die shows a 3. 3.) A fair coin is tossed three times. Find the probability of getting at least two tails, given that the first toss is tails.
You are rolling a pair of balanced dice in a board game. Rolls are independent. You...
You are rolling a pair of balanced dice in a board game. Rolls are independent. You land in a danger zone that requires you to roll doubles (both faces show the same number of spots) before you are allowed to play again. 1. What is the probability of rolling doubles on a single toss of the dice? A) 25/36 B) 5/36 C) 1/6 D) 1/36 2. What is the probability that you do not roll doubles on the first toss,...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT