Question

sock sorting problem?

Answer 1

Professor Tovey sorts his socks in the following way. He grabs a sock from the laundry basket and places it on the table. Then he grabs another sock from the basket. If it matches a sock on the table, he folds the two together and puts them away. If the sock does not match a sock on the table, he places it on the table. He continues selecting socks one at a time until all of the socks have been paired up and put away. Let us assume that his laundry basket initially has n pairs of socks. Among the 2n pairs of socks in the basket, each sock has exactly one partner. Let us assume that each time Prof. Tovey selects a sock from the basket, he selects one of the socks at random from the basket. (In this context, \at random" means that each sock remaining in the basket is equally likely to be selected.) Let us assume n = 50 so initially, there are 100 socks in the basket. (a) After Prof. Tovey has selected 50 socks from the basket, what is the probability that there are (a) no socks on the table?