Lab 4(a) - ProbabilityPart 1: Theoretical versus empirical probabilityObjective: The objective of this assignment is to compare the theoretical and empirical probabilities whenrolling two six-sided dice. This will be achieved by rolling two dice multiple times and recording theoutcomes, and then comparing the observed frequencies to the expected probabilities.Procedure for obtaining the theoretical probability:1. In the table below, write down the sample space (that is, all the possible outcomes) when 2 six-sided dice are rolled then summed. For example, the result pictured below is 8. This result hasbeen filled in everywhere it belongs within this table.1234563+5=8All possible outcomes when summing the result of rolling 2 six-sided dice1234563+5=85+3=82. Use the table above to help you compute the probability of obtaining a sum of 5 or a 6.P(5 U 6) = Lab 4(a) - ProbabilityPart 1: Theoretical versus empirical probabilityObjective: The objective of this assignment is to compare the theoretical and empirical probabilities whenrolling two six-sided dice. This will be achieved by rolling two dice multiple times and recording theoutcomes, and then comparing the observed frequencies to the expected probabilities.Procedure for obtaining the theoretical probability:1. In the table below, write down the sample space (that is, all the possible outcomes) when 2 six-sided dice are rolled then summed. For example, the result pictured below is 8. This result hasbeen filled in everywhere it belongs within this table.1234563+5=8All possible outcomes when summing the result of rolling 2 six-sided dice1234563+5=85+3=82. Use the table above to help you compute the probability of obtaining a sum of 5 or a 6.P(5 U 6) =

Analysis: 1. Does the theoretical probability match the empirical probability? Explain why this is or whether this poses a problem. 2. Fill in the blank: The Law of Large Numbers tells us that the empirical probability approaches the theoretical probability when 3. Explain how to change the Procedure for the Empirical Probability so that the empirical probability more closely resembles the theoretical probability. 4. Implement the change you proposed in the previous problem. Explain the results of this implementation below. (Include screenshots from StatCrunch.) Conclusion: In conclusion, this assignment demonstrates the difference between theoretical and empirical probabilities. Theoretical probabilities are calculated based on the number of ways an event can occur divided by the total number of possible outcomes. Empirical probabilities are calculated based on the number of times an event actually occurs. By comparing the two, we can see how closely the outcomes of an experiment match the expected probabilities.

Analysis: 1. Does the theoretical probability match the empirical probability? Explain why this is or whether this poses a problem. 2. Fill in the blank: The Law of Large Numbers tells us that the empirical probability approaches the theoretical probability when 3. Explain how to change the Procedure for the Empirical Probability so that the empirical probability more closely resembles the theoretical probability. 4. Implement the change you proposed in the previous problem. Explain the results of this implementation below. (Include screenshots from StatCrunch.) Conclusion: In conclusion, this assignment demonstrates the difference between theoretical and empirical probabilities. Theoretical probabilities are calculated based on the number of ways an event can occur divided by the total number of possible outcomes. Empirical probabilities are calculated based on the number of times an event actually occurs. By comparing the two, we can see how closely the outcomes of an experiment match the expected probabilities.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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