Last year during Thanksgiving, n people gathered at a party and played

a game together. They each took off their pair of gloves and put them into a box. After that, each one of them took two gloves randomly from the box, which contained all 2n gloves, and put them back into the box before the next person drew gloves from it. The two gloves taken out by each participant were taken out simultaneously before being put back and might or might not originally be a pair. Suppose Tim was among the n participants, what is the probability that Tim drew his pair of gloves from the box?

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