Unformatted text preview: probability that none of the three failure times are within one of each other. 5. A needle of length L < 1 is dropped randomly onto a sheet of paper with parallel lines drawn at unit distance apart. Find explicitly the probability that the needle will cut one of the parallel lines. 6. There are N molecules of benzine mixed in with a quart of water in a jar. Half the mixture is removed and replaced with half a quart of pure water. The liquid in the jar is mixed and again half of it is removed and replaced with water, and so on. Show that there is a positive number c not depending on N such that for every N there is a probability of at least c that at some time during this process exactly one molecule of benzine remains in the jar. 1...
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 Spring '09
 Math, Molecule, Randomness

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