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Undergraduate
By
Shiva Kintali
on May 22, 2013 | Updated Dec. 6, 2017
Balls and bin game
Consider the following balls-and-bin game. We start with one black ball and one white ball in a bin. We repeatedly do the following : choose one ball from the bin uniformly at random, and then put the…
Mathematics
Probability
sampling
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Undergraduate
By
True Putnam
on Aug. 28, 2013 | Updated Jan. 4, 2018
Putnam 2005 A6
Let \(n\) be given, \(n \geq 4\), and suppose that \(P_1,P_2, \dots,P_n\) are \(n\) randomly, independently and uniformly, chosen points on a circle. Consider the convex \(n\)-gon whose vertices are \…
Mathematics
Probability
uniform distribution
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Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Minimum of Random Subsets
Let \(S = \){\(1,2,\dots,n\)}. Let \(A,B\) be two random subsets of \(S\). Let \(\min(A)\) denote the minimum number in the set \(A\). What is the probability that \(\min(A)= \min(B)\) ? Evalua…
Mathematics
Probability
probability
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Undergraduate
By
Shiva Kintali
on Nov. 12, 2012 | Updated Dec. 6, 2017
Alice, Bob and children
Alice and Bob decide to have children until either they have their first girl or they have \(k \geq 1\) children. Assume that each child is a boy or girl independently with probability 1/2, and that …
Mathematics
Probability
expectation
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