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Unformatted text preview: X and Y . (c) Find ONE of P ( X = 20) , P ( Y = 20). 3. Suppose that A and B are two points chosen at random in the unit circle in R 2 . Find the probability that the circle centered at A with radius AB (i.e., radius equals the distance between A and B ) is completely contained within the unit disc. 4. Two points are picked at random from the unit square { ( x,y ) : 0 ≤ x ≤ 1 , ≤ y ≤ 1 } . Find the probability that the (inﬁnite) straight line through the two points intersects the line segment { ( x,y ) : x = 1 , ≤ y ≤ 1 } . 5. Ten white and ten black balls are divided into two boxes. What is the division that maximizes the probability that if one of the boxes is picked at random and then one ball is drawn from the box at random, the chosen ball is white? Justify your answer. 1...
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This document was uploaded on 01/25/2012.
 Spring '09
 Math

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