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Unformatted text preview: CS237. Practice Problems Set 3: Basic Probability. Not Graded. Please complete by Thurs Feb 10. February 14, 2011 Reading. Schaums Chapter 3. L&L probability- Chapter 18. Optional Extra Practice. Any of the problems in Schaumss Chapter 3. Exercise 1. You and your friend are among 10 people sitting around a round table. What is the probability you sit next to each other? Solution : You can choose a seat in 10 ways and your friend can do that in 2 ways. The rest of them can permute as they wish in 8! ways. Therefore, p = 10 2 8! 10! = 2 9 . Exercise 2. In a bin, there are n balls numbered 1 , 2 , 3 , ..., n . You draw a sequence of n balls,, one by one without replacement, i.e., once you draw a ball, you cant draw it again. with replacement, i.e., once you draw a ball, you note its position in the sequence, and then put it back in the bin, so that you can potentially choose it again later. Whats the probability that you draw the sequence 1 , 2 , 3 , 4 , ...., n ? Solution : Let us do the first one first. There is only one sequence that fits our condition. So, p = 1 /n ! . In the second case, with return we have p = 1 /n n . Exercise 3. In a bin, we have N balls numbered 1 , .., N . You draw n balls, without replacement (as explained in the previous exercise). What is the probability that the largest number you draw is k , for 1 k N ? Answer the same question assuming you draw balls with replacement (as...
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- Spring '11