Write down a precise sum expression for the probability that the first five rolls give a three at most two times. b. Calculate the probability that the first three does not appear before the fifth roll. c. Calculate the probability that the first three appears before the twentieth roll but not before the fifth roll.

A First Course in Probability (10th Edition)
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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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A fair die is rolled repeatedly. Use precise rotation of probabilities of events and random variables for the solutions to the questions below.

Write down a precise sum expression for the probability that the first five rolls give a three at most two times.

b. Calculate the probability that the first three does not appear before the fifth roll.

c. Calculate the probability that the first three appears before the twentieth roll but not before the fifth roll.

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