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3. A bag contains 12 dice: 3 of which are weighted so that instead of showing a "6" 1/6 of the ti...
Please solve this probability and statistics problem The lecturer has four 6-sided dice, of which three...
Please solve this probability and statistics problem The lecturer has four 6-sided dice, of which three are regular (results 1, ...,6 are equally probable). One die is deformed so that results 1 and 6 each have probability 0.3, and each other result has probability 0.1. The lecturer has chosen one die randomly and rolled it five times, obtaining the result sequence (6, 6, 2, 4, 6). We denote = 1 if the chosen die is regular, and = 2 if...
In Yahtzee, 5 standard dice are rolled up to three times on a given turn. A...
In Yahtzee, 5 standard dice are rolled up to three times on a given turn. A player can choose to save anywhere from 0 - 5 of the dice between rolls 1 and 2 and between rolls 2 and 3, meaning that the player can set aside certain dice before rolling the remaining dice if they choose to do so. Suppose that a given player does not take advantage of saving die rolls and instead rolls all 5 dice each...
probability a)You roll a dice with six sides. What is the probability of rolling a 3...
probability a)You roll a dice with six sides. What is the probability of rolling a 3 or a 4? b)You roll one dice, twice. What is the probability of rolling an even number the first time and a 1 the second time? c) There are ten marbles in a bag, three yellow, three blue and four red. You draw one marble out of the bag. What is the probability that the marble is yellow or blue?
Roll 6-sided dice. If “1, 2 or 3” occurs in the first roll, flip a coin....
Roll 6-sided dice. If “1, 2 or 3” occurs in the first roll, flip a coin. If “4, 5 or 6” occurs, roll 6-sided dice again. What is the sample space of this experiment, Show with the tree diagram technique. How many sample points are in the sample space? What is the probability that flips results in a head?
Problem 3. (10 points) We roll two fair 6-sided dice. (1) What is the probability that...
Problem 3. (10 points) We roll two fair 6-sided dice. (1) What is the probability that at least one die roll is 6? (2) Given that two two dice land on different numbers, what is the conditional probability that at least one die roll is a 6? Thint] You may use the graphical approach (Lecture 5 slide 11-12) to help you solve the problem.
Exercise I: More dice rolls You repeatedly throw a dice. 1. Compute the probability of the...
Exercise I: More dice rolls You repeatedly throw a dice. 1. Compute the probability of the following events. Write these events precisely using other events, and say where you use assumptions such as independence or disjoint- ness. Give your results as a single simplified fraction. (a) The first roll is even and the second one is odd. (b) The first five rolls are even. (c) The first roll is even and the second one is odd, or the first roll...
The Dice game of "Pig" can be played with the following rules. 1. Roll two six-sided dice. Add the face values...
The Dice game of "Pig" can be played with the following rules. 1. Roll two six-sided dice. Add the face values together. 2. Choose whether to roll the dice again or pass the dice to your opponent. 3. If you pass, then you get to bank any points earned on your turn. Those points become permanent. If you roll again, then add your result to your previous score, but you run the risk of losing all points earned since your...
Part 2: Weighted Dice Suppose that I have some weighted dice with the following ‘probability distribution’:...
Part 2: Weighted Dice
Suppose that I have some weighted dice with the following
‘probability distribution’:
Outcome 1 2 3 4 5 6
Probability 1/8 1/8 1/8 2/8 2/8 2/8
1) Is this a discrete or continuous probability distribution?
What is wrong with it?
2) Here is a fixed version. Verify that it is a valid
probability distribution. To do this, check that the first two
probability rules apply.
Outcome 1 2 3 4 5 6
Probability 1/9 1/9 1/9...
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. A)What is the probability you made 2 points? B)What is the probability that your friend will...
Complete each problem separately and perform in python. 1. Create a script that will roll five...
Complete each problem separately and perform in python. 1. Create a script that will roll five dice and print out their values. Allow the user to roll the dice three times. Prompt them to hit enter to roll. Ex: Hit enter to roll 1,4,3,6,6 Hit enter to roll 3,5,1,2,1 Hit enter to roll 4,3,4,2,6 2. Write a script that will roll five dice (just one time). The user's score will be the sum of the values on the dice. Print...
Please solve this probability and statistics problem The lecturer has four 6-sided dice, of which three are regular (results 1, ...,6 are equally probable). One die is deformed so that results 1 and 6 each have probability 0.3, and each other result has probability 0.1. The lecturer has chosen one die randomly and rolled it five times, obtaining the result sequence (6, 6, 2, 4, 6). We denote = 1 if the chosen die is regular, and = 2 if...
Problem 3. (10 points) We roll two fair 6-sided dice. (1) What is the probability that at least one die roll is 6? (2) Given that two two dice land on different numbers, what is the conditional probability that at least one die roll is a 6? Thint] You may use the graphical approach (Lecture 5 slide 11-12) to help you solve the problem.
Exercise I: More dice rolls You repeatedly throw a dice. 1. Compute the probability of the following events. Write these events precisely using other events, and say where you use assumptions such as independence or disjoint- ness. Give your results as a single simplified fraction. (a) The first roll is even and the second one is odd. (b) The first five rolls are even. (c) The first roll is even and the second one is odd, or the first roll...
The Dice game of "Pig" can be played with the following rules. 1. Roll two six-sided dice. Add the face values together. 2. Choose whether to roll the dice again or pass the dice to your opponent. 3. If you pass, then you get to bank any points earned on your turn. Those points become permanent. If you roll again, then add your result to your previous score, but you run the risk of losing all points earned since your...
Part 2: Weighted Dice
Suppose that I have some weighted dice with the following
‘probability distribution’:
Outcome 1 2 3 4 5 6
Probability 1/8 1/8 1/8 2/8 2/8 2/8
1) Is this a discrete or continuous probability distribution?
What is wrong with it?
2) Here is a fixed version. Verify that it is a valid
probability distribution. To do this, check that the first two
probability rules apply.
Outcome 1 2 3 4 5 6
Probability 1/9 1/9 1/9...
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