Question

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:

What is the probability that your friend will score 2 points?

Step 3 of 5:

What is the probability you score 4 or more points in this round?

Step 4 of 5:

If we play a second round of this game, what is the probability that you will have exactly 6 points at the end of the second round?

Step 5 of 5:

If we play another round what is the probability you will have 10 or more points?

Homework Answers

Answer #1

#1.
probability of getting 1, 2, 3 or 4 on any die is 4/6

In order to earn 2 points exactly 2 dice should show 1, 2 ,3 or 4

required probability = 5C2 * (4/6)^2 * (2/6)^3 = 0.1646

#2.
probability of getting 5 or 6 on any die is 2/6

In order to earn 2 points exactly 2 dice should show 5 or 6

required probability = 5C2 * (2/6)^2 * (4/6)^3 = 0.3292

#3.
in order to score 4 or more points, 4 or more dice should show 1,2,3 or 4

required probability = (5C4 * (4/6)^4 * (2/6) + 5C5 * (4/6)^5 * (2/6)^0) = 0.4609

#4.
second round means overall 10 dice are rolled

required probability = 10C6 * (4/6)^6 * (2/6)^4 = 0.2276

#3.
aother round means overall 15 dice are rolled

required probability = 15C10 * (4/6)^10 * (2/6)^5 = 0.2143

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 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:...
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...
A game consists of rolling two dice. The game costs $2 to play. You roll a...
A game consists of rolling two dice. The game costs $2 to play. You roll a two dice. If the outcome totals 9 you get $10. Otherwise, you lose your $2. Should you play the game? Explain using probability.
Bunco is a group dice game that requires no skill. The objective of the game is...
Bunco is a group dice game that requires no skill. The objective of the game is to accumulate points by rolling certain combinations. The game is played with three dice, but we will consider a simpler version involving only two dice. How do you play two dice Bunco? There are six rounds, one for each of the possible outcomes in a die, namely the numbers one through six. Going clockwise, players take turns rolling two dice trying to score points....
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?
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?
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...
1. Game of rolling dice a. Roll a fair die once. What is the sample space?...
1. Game of rolling dice a. Roll a fair die once. What is the sample space? What is the probability to get “six”? What is the probability to get “six” or “five”? b. Roll a fair die 10 times. What is the probability to get “six” twice? What is the probability to get six at least twice? c. Roll a fair die 10 times. What is the expected value and variance of getting “six”? d. If you roll the die...
You are playing another dice game where you roll just one die--this time, you lose a...
You are playing another dice game where you roll just one die--this time, you lose a point if you roll a 1. You are going to roll the die 60 times. Use that information to answer the remaining questions. A. What are the values of p and q? (Hint: notice this is binomial data, where p is the probability of losing a point and q is the probability of not losing a point.) p =    and q = B....
Chicago is a group dice game that requires no skill. The objective of the game is...
Chicago is a group dice game that requires no skill. The objective of the game is to accumulate points by rolling certain combinations (GamezBuff, 2017). How do you play Chicago? There are eleven rounds in the game, one for each combination that can be made by adding two dice, namely the numbers two through 12. Each round has a target combination starting with two and going up all the way to 12. Going clockwise, the players take turns to roll...