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4. Consider a dishonest casino that occasionally uses biased dice. The fair die is used 9 times as often as the biased one. The biased die is made so that 6 is rolled with probability 0.18, and the other five numbers are equally likely as each other. Compute the following quantities: (a) The probability that a 6 is rolled. (b) The probability that a biased die was used when a 6 is rolled. (c) The probability that a biased die used when 6 is not rolled.

4. Consider a dishonest casino that occasionally uses biased dice. The fair die is used 9 times as often as the biased one. The biased die is made so that 6 is rolled with probability 0.18, and the other five numbers are equally likely as each other. Compute the following quantities: (a) The probability that a 6 is rolled. (b) The probability that a biased die was used when a 6 is rolled. (c) The probability that a biased die used when 6 is not rolled.

A First Course in Probability (10th Edition)
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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4. Consider a dishonest casino that occasionally uses biased dice. The fair die is used 9 times as often as the biased one. The biased die is made so that 6 is rolled with probability 0.18, and the other five numbers are equally likely as each other. Compute the following quantities: (a) The probability that a 6 is rolled. (b) The probability that a biased die was used when a 6 is rolled. (c) The probability that a biased die used when 6 is not rolled. (d) The number of 6's in a row we would need to see before it is more likely that we had been using the biased die.
Transcribed Image Text:4. Consider a dishonest casino that occasionally uses biased dice. The fair die is used 9 times as often as the biased one. The biased die is made so that 6 is rolled with probability 0.18, and the other five numbers are equally likely as each other. Compute the following quantities: (a) The probability that a 6 is rolled. (b) The probability that a biased die was used when a 6 is rolled. (c) The probability that a biased die used when 6 is not rolled. (d) The number of 6's in a row we would need to see before it is more likely that we had been using the biased die.
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