6. The Chevalier Problem (At least one generalized):(a) First problem: Find the probability of rolling at least one 6 in four rolls of a standard six-sideddie.(b) Second problem: Find the probability of rolling at least one double-6 in 24 rolls of two six-sideddice.(c) Comment on how the difference between the probabilities gotten above can be the differencebetween rags and riches in gambling. How can casinos exploit this idea?PrintA Alternative formatsActivity Detailsviewed this topicar 13, 2022 2:55 PMDD4480F10F5%247* 00

Introduction: Denote X as the number of rolls resulting in a 6 when a standard six-sided die is…

Answered: 6. The Chevalier Problem (At least one…

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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Your friend rolls an "unusual" six-sided die many times. She reports the probabilities of the possible outcomes are about as follows: Number Rolled: 1 2 3 4 5 6 Probability: 0.20 0.20 0.10 0.10 0.10 (a) Complete the table above by calculating the probability of rolling a 4. (b) Your friend creates the following game using this "unusual" die. You will pay her $2 if she rolls an even number and she will pay you $3 if she rolls an odd number.Use the table from part (a) to fill in the probability model below: Outcome: Roll an even number Roll and odd number Amount: Probability: (c) What is the expected value of this game for you? (d) Is this a fair game, meaning that each of you can expect to win the same amount in the long run? Explain.
Two six-sided dice were rolled, and a friend tells us that the numbers that came up were identical. Find the probability that the sum of the numbers was as follows. (Enter your probabilities as fractions.) (a) 8 (b) 7 (c) an even number (d) an odd number
(a) What is the probability that a fair coin lands tails up eight times in a row? (b) Suppose you're offered a bet at 250:1 odds against a fair coin landing tails up eight times in a row. What would you do-take one side of the bet or the other, or decide not to play at all? (Your answer should depend both on your answer to the previous part of the problem and on your own personal ideas about risk and money.) (c) Answer the previous question if you are operating a casino. Compute the house advantage and explain how much money you would make in the long run. (d) Which is more likely, that eight flips will be TTTTTTTT or that they will be THTHTHTH?
.Seven six-sided dice are rolled. Find the following probabilities.(a) The probability that at least one of the dice rolled is showing a six.(b) The probability that the sum of the dice is greater than 8.
In this problem, the gambler’s idea of odds does not enter at all. a. The odds of an event are 1/5. What is the probability of the event occurring? b. The probability of an event is 2/3. What are the odds of the event occurring?
An experiment is rolling two fair dice. What is the probability that the sum is 6?
2 questions, first one is (a) and the second one is (b)
A geologist has collected 19 specimens of basaltic rock and 19 specimens of granite. The geologist instructs a laboratory assistant to randomly select 33 of the specimens for analysis. (a) What is the pmf of the number of granite specimens selected for analysis? (Round your probabilities to four decimal places.) P(x) (b) What is the probability that all specimens of one of the two types of rock are selected for analysis? (Round your answer to four decimal places.) (c) What is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value? (Round your answer to four decimal places.)
In the experiment of rolling two unloaded dice. What is the probability that the sum of the two dice is 2?

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