Question

A bar has a dice game that works as follows: You simultaneously roll 5 dice, and...

A bar has a dice game that works as follows: You simultaneously roll 5 dice, and if all 5 dice are the same value, you win. If your dice are not all the same, you get to re-roll all 5 dice again. You get three tries in total. What is the probability of winning? That is, what is the probability that in your three tries, at least one of your rolls consists of five-of-a-kind?

Homework Answers

Answer #1

Probability of getting 1 in all 5 dice is 1/6*1/6*1/6*1/6*1/6 = 1/6^5

Probability of getting 2 in all dice = 1/6^5

Similarly probability of getting 3,4,5,6 in all 5 dice is also 1/6^5

So total probability of winning in a single throw is 6/(6)^5 = 1/6^4

Probability of losing is 1-1/6^4

Now according to problem we have 3 throws

Probability of atleast on throw getting same numbers is = 1- probability of not getting all same numbers in any throw

= 1- 3C0(1/6^4)^0*(1-1/6^4)^3 = 0.0023

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
You simultaneously roll 5 dice, and if all 5 dice are the same value, you win....
You simultaneously roll 5 dice, and if all 5 dice are the same value, you win. If your dice are not all the same, you get to re-roll all 5 dice again. You get three tries in total. What is the probability of winning? That is, what is the probability that in your three tries, at least one of your rolls consists of five-of-a-kind?
. A dice game is played as follows: you pay one dollar to play, then you...
. A dice game is played as follows: you pay one dollar to play, then you roll a fair six-sided die. If you roll a six, you win three dollars. Someone claims to have won a thousand dollars playing this game nine thousand times. How unlikely is this? Find an upper bound for the probability that a person playing this game will win at least a thousand dollars.
You and a friend are rolling a set of 5 dice. The game works such that...
You and a friend are rolling a set of 5 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 1 of 5: What is the probability you made 2 points? Step 2 of 5:...
Problem 4)A simplified version of the dice game 10,000 is played using 5 dice. The player...
Problem 4)A simplified version of the dice game 10,000 is played using 5 dice. The player rolls the 5 six-sided dice, each 1 that is rolled, the player achieves a score of 100. A) How many possible ways are there to roll i l's over these 5 dice? (Hint: use combinations) B) The probability of any one dice rolling to a value of 1 is 1/5 (since each dice has six sides). Use the binomial probability distribution. Calculate the probability...
The following describes a dice game played at a carnival. The game costs $5 to play....
The following describes a dice game played at a carnival. The game costs $5 to play. You roll the die once. If you roll a one or a two, you get nothing. If you roll a three or a four, you get $4 back. If you roll a five you get your $5 back and if you roll a six, you receive $12. What is your Expected Value? Should you play the game?
You and a friend are rolling a set of 6 dice. The game works such that...
You and a friend are rolling a set of 6 dice. The game works such that if a die shows the values 1, 2, or 3 you will get a point for that die. Each die that shows 4, 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 1 of 5: What is the probability you made 2 points? Step 2 of 5:...
Players A and B take turns at rolling two dice, starting with A. The first person...
Players A and B take turns at rolling two dice, starting with A. The first person to get a sum of at least 9 on a roll of the two dice wins the game. Find the probability that A will win the game if: (a) the game is just about to begin (b) 8, 4, 3, 7 and 7 have already been rolled (c) a draw is to be declared in the event of no-one winning within 6 rolls.
Players A and B take turns at rolling two dice, starting with A. The first person...
Players A and B take turns at rolling two dice, starting with A. The first person to get a sum of at least 9 on a roll of the two dice wins the game. Find the probability that A will win the game if: (a) the game is just about to begin (b) 8, 4, 3, 7 and 7 have already been rolled (c) a draw is to be declared in the event of no-one winning within 6 rolls.
You and a friend are rolling a set of 7 dice. The game works such that...
You and a friend are rolling a set of 7 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. A)What is the probability you made 2 points? B)What is the probability that your friend will...
I propose to you a game. You roll 2 dice. If the sum of the numbers...
I propose to you a game. You roll 2 dice. If the sum of the numbers showing is either 6, or 7, or 8, I win. If it is 2, 3, 4, 5, 9, 10, 11, 12, you win. Since you have lots more possible winning combinations than I do, the rules are that you pay me $2.00 when I win and I pay you $1.00 when you win. If we play this game 30 times, how much do you...