5500HW2 - ORIE 3500/5500 Fall Term 2008 Assignment 2 Note...

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ORIE 3500/5500 Fall Term 2008 Assignment 2 Note that the due date is Monday, September 22 , at 1:00 pm you need to mention your section number on the top of your answer script. 1. [2 + 2 + (2 + 2 + 2) = 10 pts] Three friends went in a forest to hunt a deer. They can hit the target with a bullet with probabilities 0.3, 0.4, and 0.5, respectively. They saw a deer and fired simultaneously and independently. (a) What is the probability that all of them hit the deer? (b) What is the probability that exactly two of them hit the deer? (c) If exactly one bullet hit the deer, then what are the probabilities that the deer was killed by the first/second/third friend? 2. [3 + 3 + 4 = 10 pts] Suppose you have two urns. In the first urn there are 5 blue balls and 10 green balls. In the second urn there are 4 blue balls and 9 green balls. A ball is chosen at random from the first urn and put in the second urn. Then a second ball is chosen from the second urn. (a) What is the probability that the second ball is blue?
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5500HW2 - ORIE 3500/5500 Fall Term 2008 Assignment 2 Note...

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