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Bonus +4 Suppose you roll six dice at once and are asked to find the probability that a 4 was rolled on at least one die. Bob makes the following argument: "The probability of getting a 4 when rolling a fair six-sided die is 1/6. So if I roll six different dice all at once, the probability of getting a 4 on at least one die is like doing '4 or 4 or 4 or 4 or 4 or 4'. Since 'or means 'add', the total probability of getting a 4 at least once in those six throws should be 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1= 100%. This means that I am guaranteed to get at least one 4!" That can't be right. Surely it's at least possible not to get a 4 if you roll six dice! But Bob's argument seems quite persuasive. Can you see what's wrong with it? Hint: this is hard! Think about over-counting. Extra bonus +2 Calculate the actual probability of rolling six dice and getting a 4 at least once.

Bonus +4 Suppose you roll six dice at once and are asked to find the probability that a 4 was rolled on at least one die. Bob makes the following argument: "The probability of getting a 4 when rolling a fair six-sided die is 1/6. So if I roll six different dice all at once, the probability of getting a 4 on at least one die is like doing '4 or 4 or 4 or 4 or 4 or 4'. Since 'or means 'add', the total probability of getting a 4 at least once in those six throws should be 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1= 100%. This means that I am guaranteed to get at least one 4!" That can't be right. Surely it's at least possible not to get a 4 if you roll six dice! But Bob's argument seems quite persuasive. Can you see what's wrong with it? Hint: this is hard! Think about over-counting. Extra bonus +2 Calculate the actual probability of rolling six dice and getting a 4 at least once.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Bonus +4 Suppose you roll six dice at once and are asked to find the probability that a 4 was rolled on at least one die. Bob makes the following argument: "The probability of getting a 4 when rolling a fair six-sided die is 1/6. So if I roll six different dice all at once, the probability of getting a 4 on at least one die is like doing ʻ4 or 4 or 4 or 4 or 4 or 4'. Since 'or means 'add', the total probability of getting a 4 at least once in those six throws should be 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 =1= 100%. This means that I am guaranteed to get at least one 4!" That can't be right. Surely it's at least possible not to get a 4 if you roll six dice! But Bob's argument seems quite persuasive. Can you see what's wrong with it? Hint: this is hard! Think about over-counting. Extra bonus +2 Calculate the actual probability of rolling six dice and getting a 4 at least once.
Transcribed Image Text:Bonus +4 Suppose you roll six dice at once and are asked to find the probability that a 4 was rolled on at least one die. Bob makes the following argument: "The probability of getting a 4 when rolling a fair six-sided die is 1/6. So if I roll six different dice all at once, the probability of getting a 4 on at least one die is like doing ʻ4 or 4 or 4 or 4 or 4 or 4'. Since 'or means 'add', the total probability of getting a 4 at least once in those six throws should be 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 =1= 100%. This means that I am guaranteed to get at least one 4!" That can't be right. Surely it's at least possible not to get a 4 if you roll six dice! But Bob's argument seems quite persuasive. Can you see what's wrong with it? Hint: this is hard! Think about over-counting. Extra bonus +2 Calculate the actual probability of rolling six dice and getting a 4 at least once.
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