1.1.5 A die is 'fixed' so that each time it is rolled the score cannot be the same as the preceding score, all other scores having probability 1/5. If the first score is 6, what is the probability p that the nth score is 6? What is the probability that the nth score is 1?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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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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1.1.5 A die is 'fixed' so that each time it is rolled the score cannot be the same as
the preceding score, all other scores having probability 1/5. If the first score is 6,
what is the probability p that the nth score is 6? What is the probability that the
nth score is 1?
Suppose now that a new die is produced which cannot score one greater (mo d 6)
than the preceding score, all other scores having equal probability. By considering
the relationship between the two dice find the value of p for the new die.
Transcribed Image Text:Only need the second part 1.1.5 A die is 'fixed' so that each time it is rolled the score cannot be the same as the preceding score, all other scores having probability 1/5. If the first score is 6, what is the probability p that the nth score is 6? What is the probability that the nth score is 1? Suppose now that a new die is produced which cannot score one greater (mo d 6) than the preceding score, all other scores having equal probability. By considering the relationship between the two dice find the value of p for the new die.
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