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Write a plain text e-mail to me. This homework requires no special symbols or wordprocessor features. (Do not attach a wordprocessor file such as Microsoft Word or a Excel spreadsheet. I will not read them.) Give the mail the subject "01CN101 Homework #3 by <your name>" in hankaku romaji and send it to math-hw@turnbull.sk.tsukuba.ac.jp. (This subject is helpful for automatically sorting incoming mail.)
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In problems 1 to 4, the event A1 = { the sum of a pair of 6-sided dice is 1 }, and A2, ..., A50 are defined in the same way (the number of the set is the sum). Similarly, B1 = { the product of a pair of 6-sided dice is 1 }, and B2, ..., B50 are defined in the same way.
Describe the event C = { the sum of a pair of dice is equal to their product } in terms of the events Ai and Bj.
Compute the event C from problem 1 as a set of ordered pairs of numbers. Explain the method you used to compute this set.
What is the probability of the event C? What assumptions do you need to make to compute this probability?
Are {A1, ..., A50} and {B1, ..., B50} partitions of U = { all the ways two 6-sided dice can fall }? Explain why or why not. If they are both partitions, are they the same partition?
Mr. X is a student in this class. Describe three different ways of assessing the probability that Mr. X will fail to attend class on June 15.
For each method, explain any assumptions you need to make to justify using the method.