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vo sixes in a row. Your task =, required to roll two sixes init

vo sixes in a row. Your task =, required to roll two sixes init

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterP: Prologue: Calculator Arithmetic
Section: Chapter Questions
Problem 2E: Pet Owners According to the Humane Society, in 2015, 65% of U.S. households owned at least one pet,...
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Calculate the average number of rolls of one dice, required to roll two sixes in a row. Instructions how to proceed: a) assignment means that we will roll the dice until two sixes fall in a row. Of course, these Sixes will only fall in the last two throws, and that's when we finish. Number of throws, what we did is the number of throws needed to roll two sixes in a row. Your task is to calculate the average number of rolls of one dice, required to roll two sixes after myself. We get the average number by repeating said experiment infinite number of times and calculate the average of the results obtained b) Let's call "a;" the probability that with consecutive rolls of "i" one die will not fall out twice in a row six, and with the last roll six will fall out. Let's call "b;" the probability that with consecutive rolls of "i" one die will not fall out twice in a row six, and with the last roll six will not fall out c) Probabilities "a;" and "b;" form sequences {a;}X=o and {b¡}k=o 100 Their first terms are ao = 0 and bo = 1. Construct a system of recurrent relationships for {a;}-o and {b;}%=0 sequences and find the forming functions a(x) and b(x) for these sequences. d) Let's designate "p;"the probability of falling in "į" consecutive rolls with one dice exactly once two sixes in a row in the last two throws. e) The probabilities of pi form a sequence {p;}=0 whose first terms are p, = 0 and p, = 0. Find the generating function p(x) for the sequence {p}}%=0 f) The average number of rolls of one dice required to roll two sixes in a row is calculated as: Efo i. Pi (1) P = Formula (1) is easy to prove, but that's not your job. Take Formula (1) as a given fact. g) using Formula (1) Calculate the average number of rolls of one dice required to throw two sixes in a row.
Transcribed Image Text:Calculate the average number of rolls of one dice, required to roll two sixes in a row. Instructions how to proceed: a) assignment means that we will roll the dice until two sixes fall in a row. Of course, these Sixes will only fall in the last two throws, and that's when we finish. Number of throws, what we did is the number of throws needed to roll two sixes in a row. Your task is to calculate the average number of rolls of one dice, required to roll two sixes after myself. We get the average number by repeating said experiment infinite number of times and calculate the average of the results obtained b) Let's call "a;" the probability that with consecutive rolls of "i" one die will not fall out twice in a row six, and with the last roll six will fall out. Let's call "b;" the probability that with consecutive rolls of "i" one die will not fall out twice in a row six, and with the last roll six will not fall out c) Probabilities "a;" and "b;" form sequences {a;}X=o and {b¡}k=o 100 Their first terms are ao = 0 and bo = 1. Construct a system of recurrent relationships for {a;}-o and {b;}%=0 sequences and find the forming functions a(x) and b(x) for these sequences. d) Let's designate "p;"the probability of falling in "į" consecutive rolls with one dice exactly once two sixes in a row in the last two throws. e) The probabilities of pi form a sequence {p;}=0 whose first terms are p, = 0 and p, = 0. Find the generating function p(x) for the sequence {p}}%=0 f) The average number of rolls of one dice required to roll two sixes in a row is calculated as: Efo i. Pi (1) P = Formula (1) is easy to prove, but that's not your job. Take Formula (1) as a given fact. g) using Formula (1) Calculate the average number of rolls of one dice required to throw two sixes in a row.
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