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Unformatted text preview: NTHU MATH 2810 Midterm Examination Oct 30, 2007 Note. There are 7 problems in total. To ensure consideration for partial scores, write down intermediate steps where necessary. 1. (a) ( 3pts ) Two years ago, Santa Claus was distributing 10 identical candies to 4 children at the mall. Being a kind-hearted soul, he figured he would give at least one candy to each child, but other than that he could give any number of the candies to any of the children. How many ways were there for Santa Claus to have distributed his candies? (b) ( 3pts ) Santa Claus was back at the mall last year, but that time he brought 10 different books for the 4 kids. But no more “mister nice guy,” he was willing to give some kids no books! How many ways were there for him to distribute his books that time? 2. ( 8pts ) Suppose that A and B are two events such that P ( A ∪ B ) = 3 × P ( B ) , P ( A ∩ B ) = 0 . 4 × P ( A ∩ B c ) , P (( A ∪ B ) c ) = 0 . 1 ....
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