You are now ready to tackle some questions regarding the Buffon experiment.


QUESTION 1: What is the probability that a randomly-thrown pencil will intersect a line? [ Hint: the intersection will occur if y is sufficiently small for a given angle . Find the constraint describing this relationship between y and . Integrate the joint probability over the region defined ].

QUESTION 2: Redo the above analysis assuming that the random variable Y is the distance from the center of the pencil to the next "southern" parallel line (so that 0 Y d).

QUESTION 3: Solve the Buffon needle (pencil) problem for the case in which the pencil is unrestricted in length. (This requires an analysis of the case l > d.)





GOOD LUCK!
You should get, as answer to Question 1, 2l / ( d).

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