Problem 16 Consider the following variant of Buffon s needle problem (Example 3.11) , which was investigated by Laplace. needle of length is dropped On plane surface that is partitioned in rectangles by horizontal lines that are apart and vertical lines that are b apart. Suppose that the needle s length satisfies / < a and / < b. What is the expected number of rectangle sides crossed by the needle? What is the probability that the needle will cross at least one side of some rectangle?
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