You and a friend are playing a game. You alternate turns rolling a single die, and the first person to roll a 1 or a 2 wins. Your friend goes first.
a. What’s the probability that the game ends in three rolls or fewer?
b. What’s the expected number of rolls?
c. What’s the probability that your friend wins?
You and a friend are playing a game. You alternate turns rolling a single die, and...
4. Alice and Bob take turns rolling a fair six sided die. They keep playing this game until someone gets a 6, and that person is declared the winner. Alice goes first. Find the probability that Alice wins the game. Hint: The probability should be more than 0.5 Example of Alice winning in 5 turns: В А В А 2 2 6
You and a friend are rolling a seet of 7 die. 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 a 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 that YOU made 2 points? Step 2 of 5:...
15. Your friend challenges you to a game. She says that she is going to roll 2 6-sided dice. If the first die rolls at least 5, you win if the second die rolls less than 5. If the first die rolls less than 5, you win if the second die rolls at least 5. This seems fair. Is it? (a) What is the probability that you win this game? To incentivize you, your friend says that she will pay...
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)If we play a second round of this game, what is the probability that you will...
Please show work :) Will upvote/rate! 3. Discrete Random Variables You have a biased die, where the probability that a number n appears on the die when it is rolled is defined as a random variable X such that Р(X %3D п) — с:п Here c is a positive real number. Now answer the questions below: (a) Find the value of c (b) What is the expected value of the random variable X? (c) Find how close a number you...
Using MATlLab You are playing the board game “Risk” when your friend asks you: “Do you think it is more likely to roll a total of eight or nine when rolling three dice?” Develop a program to determine if the probability of rolling an eight or a nine is greater To do this, you will need to check every possible combination of dice rolls (for example: 1-1-1, 1-2-3, 6-6-6) Hint: Nested for loops to count rolls of eight and nine...
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. A)What is the probability you made 2 points? B)What is the probability that your friend will...
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...
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...
Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. What is the probability that both die roll ones? What is the probability that exactly one die rolls a one? What is the probability that neither die rolls a one? What is the expected number of ones? If you did this 1000 times, approximately how many times would you expect that exactly one die would roll...