A dice problem. Suppose there is a 3-sided die whose equally likely outcomes are 1,2 and...

A dice problem. Suppose there is a 3-sided die whose equally likely outcomes are 1,2 and 3 after it is thrown. (A 3D object with equilateral triangle cross-sections and rounded sides might work in practice.) We have three such dice, one orange, one black, and one red. They are all put in a cup, shaken, and tossed onto a table. (a) How many elementary events (individual outcomes) are there for this experiment? (b) Write out the sample space for this experiment. (c) What is the probability that all the dice show odd numbers? All even numbers? (d) Find the probability that the sum of the three dice is 4. Do the same for sums of 8 and 9. (e) Which sum of the three dice is the most likely?

Suppose no 3 sided dice are available. How could we perform the experiment in problem 2 with regular 6-sided dice? Be careful here!

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orchestra answered 2 years ago

are the outcomes of three rolled dice equally likely

Two 6-sided dice are rolled. One die is a standard die, and the other is a...

Two 6-sided dice are rolled. One die is a standard die, and the other is a Fibonacci die with sides 1, 1, 2, 3, 5, and 8. a. What is the probability distribution of this experiment? b. What is the shape of the probability distribution? c. What is the expected value when these 2 dice are rolled?

Suppose that a sample space consists of ? equally likely outcomes. Select all of the statements...

Suppose that a sample space consists of ? equally likely outcomes. Select all of the statements that must be true. a. Each outcome in the sample space has equal probability of occurring. b. Any two events in the sample space have equal probablity of occurring. c. The probability of any event occurring is the number of ways the event can occur divided by ?. d. Probabilities can be assigned to outcomes in any manner as long as the sum of...

Suppose a red six-sided die, a blue six-sided die, and a yellow six-sided die are rolled....

Suppose a red six-sided die, a blue six-sided die, and a yellow six-sided die are rolled. Let - X1 be the random variable which is 1 if the numbers rolled on the blue die and the yellow die are the same and 0 otherwise; - X2 be the random variable which is 1 if the numbers rolled on the red die and the yellow die are the same and 0 otherwise; - X3 be the random variable which is 1...

Consider a six-sided fair dice. Complete the following tables for this die: Number on the dice...

Consider a six-sided fair dice. Complete the following tables for this die: Number on the dice Number of times it appears on the dice Relative frequency of seeing that number 1 2 3 4 5 6 Total This is the entire question, does not say how many times the dice is thrown

Suppose a 6-sided die and a 7-sided die are rolled. What is the probability of getting...

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Part 1: Two 6-sided dice are rolled. One die is a standard die, and the other...

Part 1: Two 6-sided dice are rolled. One die is a standard die, and the other is a Fibonacci die with sides 1, 1, 2, 3, 5, and 8. Submit a file with the probability distribution for this experiment. Part 2: Two 6-sided dice are rolled. One die is a standard die, and the other is a Fibonacci die with sides 1, 1, 2, 3, 5, and 8. What is the shape of the probability distribution? Part 3: Two 6-sided...

Suppose you roll two twenty-five-sided dice. Let X1, X2 the outcomes of the rolls of these...

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Suppose you are rolling a fair four-sided die and a fair six-sided die and you are...

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. a) Distinguish between the outcomes and events. b) What is the probability that both die roll ones? c) What is the probability that exactly one die rolls a one? d) What is the probability that neither die rolls a one? e) What is the expected number of ones? f) If you did this 1000 times, approximately...

Dice Suppose that a red die and a green die are rolled and the numbers on...

Dice Suppose that a red die and a green die are rolled and the numbers on the sides that face upward are observed. (See Example 7 of this section and Example 2 of the first section.) (a) What is the probability that the numbers add up to 9? (b) What is the probability that the sum of the numbers is less than S?

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