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What is the difference between scalar multiplication and matrix multiplication? Give examples of each operation.
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I need some assistance solving a Probability Theory problem. The question is broken down into two parts.
The Question is:
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. Points are usually awarded as such: 21 points if both dice match the current round number (a "Bunco"); five points are awarded if both dice match each other, but do not match the current round number (a "Mini Bunco"). Finally, one point is awarded for a single die matching the current round number.
If points are scored, the player gets to roll again, continuing to add to their score. If no points are awarded, the player's turn ends and the dice are passed to the next player.
At the end of the game, the winners get prizes for accomplishments such as the highest score, the lowest score, or the most buncos.
Part I: Complete the following steps assuming the round number is 6:
What is the probability that the player rolls two distinct numbers different than six or rolls exactly one six (no points or one point)?
What is the probability that the player rolls two of the same number but no six, i.e., two 1s, or two 2s, and so on (five points Mini Bunco)?
What is the probability that the player rolls two 6s (21 points Bunco)?
Compute the total of the probabilities found in the three previous questions.
If the player wins a dollar for every point, he/she gets and losses three dollars for getting no points, what are the expected winnings or losses on each roll?
Part II: Based on your work in Part I, discuss the following:
Describe the sample space when rolling two dice once. How can identifying all the elements of the sample space help you answer the questions in Part I?
Determine if “rolling two different numbers different than six” or “rolling exactly one six” are mutually exclusive events. Justify your answer. Explain how this information can help you answer question one, Part I.
Describe the relationship between odds and probability. Explain how you can use the result in question three, Part I to find the odds of getting a Bunco in a single roll.
What does the result found in question four, Part I imply about these events? Explain how you have used the answers to questions one and two, Part I to get the answer to question three, Part I.
Interpret the answer to question five, Part I.
Discuss the advantages of understanding probabilities when playing dice games.
Think of another scenario where probabilities can be used. Discuss the advantages of using probabilities in the context of the scenario you created.
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MTH 109 CSU Applying Probability Theory to Real World Scenario Discussion Questions
I need some assistance solving a Probability Theory problem. The question is broken down into two parts.
The Question is:
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. Points are usually awarded as such: 21 points if both dice match the current round number (a "Bunco"); five points are awarded if both dice match each other, but do not match the current round number (a "Mini Bunco"). Finally, one point is awarded for a single die matching the current round number.
If points are scored, the player gets to roll again, continuing to add to their score. If no points are awarded, the player's turn ends and the dice are passed to the next player.
At the end of the game, the winners get prizes for accomplishments such as the highest score, the lowest score, or the most buncos.
Part I: Complete the following steps assuming the round number is 6:
What is the probability that the player rolls two distinct numbers different than six or rolls exactly one six (no points or one point)?
What is the probability that the player rolls two of the same number but no six, i.e., two 1s, or two 2s, and so on (five points Mini Bunco)?
What is the probability that the player rolls two 6s (21 points Bunco)?
Compute the total of the probabilities found in the three previous questions.
If the player wins a dollar for every point, he/she gets and losses three dollars for getting no points, what are the expected winnings or losses on each roll?
Part II: Based on your work in Part I, discuss the following:
Describe the sample space when rolling two dice once. How can identifying all the elements of the sample space help you answer the questions in Part I?
Determine if “rolling two different numbers different than six” or “rolling exactly one six” are mutually exclusive events. Justify your answer. Explain how this information can help you answer question one, Part I.
Describe the relationship between odds and probability. Explain how you can use the result in question three, Part I to find the odds of getting a Bunco in a single roll.
What does the result found in question four, Part I imply about these events? Explain how you have used the answers to questions one and two, Part I to get the answer to question three, Part I.
Interpret the answer to question five, Part I.
Discuss the advantages of understanding probabilities when playing dice games.
Think of another scenario where probabilities can be used. Discuss the advantages of using probabilities in the context of the scenario you created.
133 pages
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Exploring applied optimization problems that minimize travel time.Part I: Complete the following steps:Read Example 4.34 i ...
Calculus Colorado State University Minimize Travel Time Discussion
Exploring applied optimization problems that minimize travel time.Part I: Complete the following steps:Read Example 4.34 in Section 4.7 of Calculus, Volume 1.Consider the following scenario:A lifeguard is at point A of a circular pool with diameter 40 m. He must reach someone who is drowning on the exact opposite side of the pool, at position C. The lifeguard swims with a speed v = 3 m/s from point A to point B, and then runs around the pool from point B to point C at speed w = 9 m/s.Find a function that measures the total amount of time it takes to reach the drowning person as a function of the swim angle, θ expressed in radians.Find at what angle θ, in radians, the lifeguard should swim to reach the drowning person in the least amount of time.What is the domain of the function you created in part (a)?Part II: Based on your work in Part I, discuss the following:How do you know that the function you created in Part I has a maximum and minimum value?Discuss how your answers to Part I would be affected if the diameter of the pool increased.For what running speed would it be faster to swim the entire time? What angle would correspond to this scenario?For what angle, , would it take the longest to reach the drowning person?Suppose the pool was rectangular. Respond to the following:Does it still make sense to parameterize using ? Why or why not?If not, what parameter would you use?If so, how does the parameterization change?Set up, but do not solve, this problem with a rectangular pool.Answer the following questions that reference Example 4.34:How do we know that the function T(x) has a maximum and minimum?What restrictions are there on what the domain of T can be in this scenario?Elaborate, in your own words, on why we must evaluate T(0) and T(6).
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