When we roll one die, we have a 1 in 6 probability of getting any particular...

When we roll one die, we have a 1 in 6 probability of getting any particular number on the die. When we roll a pair of dice, there are 36 different pairs that can be produced, yet only 11 actual distinct values.

Explain how the probability associated with the roll of each individual die in the pair explains the higher variability in the total outcome of the roll of each pair. How do the concepts of permutations and combinations apply to this example? Discuss how the notion of degree of freedom can be used to illustrate the accumulating results of a set of dice rolls.

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orchestra answered 2 years ago

When we roll one die, we have a 1 in 6 probability of getting any particular...

When we roll one die, we have a 1 in 6 probability of getting any particular number on the die. When we roll both dice, there are 36 different permutations of total pairs that can be produced, yet only 11 actual distinct values. Explain how the probability associated with the roll of each individual die in the pair explains the higher variability in the total outcome of the roll of each pair. Discuss how this affects what you think about...

1. Assume we roll 6 dice. What is the probability that the roll contains: a. 6...

1. Assume we roll 6 dice. What is the probability that the roll contains: a. 6 of the same number b. 3 of one number, 2 of a second number, and 1 non-matching number c. 3 pairs of different numbers

If one dice is rolled (die 1, die 2), find the probability of getting sum less...

If one dice is rolled (die 1, die 2), find the probability of getting sum less than 11? a. What is the probability experiment? Rolling a dice (die 1, die 2) b. What is the event(s)? sum greater than 11 c. What technique can I use to solve this problem? Select an answer d. How do you know you can use that technique? Select an answer f. Find the probability of rolling a sum that is sum less than 11....

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

Suppose a 6-sided die and a 7-sided die are rolled. What is the probability of getting sum less than or equal to 5 for the first time on the 4th roll? Show your work to receive credit.

Create a die, which will roll a 6 with probability of 50% and all other numbers...

Create a die, which will roll a 6 with probability of 50% and all other numbers (1-5) with equal probability. What is E(Y) if Y was the outcome of that die? and X is the result of the fair die. sd(Y) var(X-2Y) Please write the code in R

Suppose that we roll a die 166 times. What is the approximate probability that the sum...

Suppose that we roll a die 166 times. What is the approximate probability that the sum of the numbers obtained is between 544 and 606, inclusive. (if possible, could you explain the steps/ state theorems used). Thank you :)

we will roll a standard six-sided die and try to estimate the probability that each number...

we will roll a standard six-sided die and try to estimate the probability that each number will come up. If it is a fair die, each number should come up 1/6th of the time. 1. Collecting the data Put a die in a cup and roll it 30 times. With each roll, record what value came up and list the totals in the table below. For each number the Relative frequency = # of times the number occurs / #...

You roll one blue 6-sided die, and one red 4-sided die. Let A be the event...

You roll one blue 6-sided die, and one red 4-sided die. Let A be the event that the outcome of the red die is twice the outcome on the blue die Let B be the event that the outcome of the blue die is greater than the outcome on the red die Let C be the event that the sum of the two dice is a prime number. a) Find P(B) and P(C) by clearly listing all outcomes in B...

The newest invention is a three-sided die. On any roll of this die, the result is...

The newest invention is a three-sided die. On any roll of this die, the result is 1 with probability 1/2, 2 with probability 1/4, and 3 with probability 1/4. Consider a sequence of six independent rolls of this die. A. Find the probability that exactly two of the rolls result in a 3. B. Given that exactly two of the six rolls resulted in a 1, find the probability that the first roll resulted in a 1. C. We are...

Find the conditional probability, in a single roll of two fair 6-sided dice, that neither die...

Find the conditional probability, in a single roll of two fair 6-sided dice, that neither die is a three,given that the sum is greater than 7.

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When we roll one die, we have a 1 in 6 probability of getting any particular...

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When we roll one die, we have a 1 in 6 probability of getting any particular...

1. Assume we roll 6 dice. What is the probability that the roll contains: a. 6...

If one dice is rolled (die 1, die 2), find the probability of getting sum less...

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

Create a die, which will roll a 6 with probability of 50% and all other numbers...

Suppose that we roll a die 166 times. What is the approximate probability that the sum...

we will roll a standard six-sided die and try to estimate the probability that each number...

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Find the conditional probability, in a single roll of two fair 6-sided dice, that neither die...