Repeatedly rolling a die would result in a uniform distribution of values between 1 and 6, inclusive. Repeatedly rolling two (2) dice would result in a uniform distribution of values between two (2) and twelve (12) inclusive. a. In this simulation, repeatedly roll one (1) die, count the number of occurrences of each value and plot the histogram: 1. After 100 simulations. ii. After 1,000 simulations. b. In the next simulation, repeatedly roll four (4) dice, sum the results of the four (4) dice faces, count the number of occurrences of each value and plot the histogram: i. After 100 simulations. ii. After 1,000 simulations. Each simultaneous roll of four (4) dice is counted as one simulation. c. Compute the following probabilities based on your simulations: If one die is rolled what is the probability that i. The outcome is even? The outcome is odd? ii. If four dice are rolled what is the probability that • The total showing is even? • The total showing is odd? probability of occurrence of event i = number of times event i occurred total number of simulations

Repeatedly rolling a die would result in a uniform distribution of values between 1 and 6, inclusive. Repeatedly rolling two (2) dice would result in a uniform distribution of values between two (2) and twelve (12) inclusive. a. In this simulation, repeatedly roll one (1) die, count the number of occurrences of each value and plot the histogram: 1. After 100 simulations. ii. After 1,000 simulations. b. In the next simulation, repeatedly roll four (4) dice, sum the results of the four (4) dice faces, count the number of occurrences of each value and plot the histogram: i. After 100 simulations. ii. After 1,000 simulations. Each simultaneous roll of four (4) dice is counted as one simulation. c. Compute the following probabilities based on your simulations: If one die is rolled what is the probability that i. The outcome is even? The outcome is odd? ii. If four dice are rolled what is the probability that • The total showing is even? • The total showing is odd? probability of occurrence of event i = number of times event i occurred total number of simulations

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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