The color of the last card

Question

A standard 52-card deck is shuffled uniformly at random and dealt one card at a time, face up.

What is the probability that the last card dealt is a spade? And what is the probability that the 40th card dealt is the ace of spades specifically?

Accepted Answer

Both answers fall out of one idea: in a uniform shuffle, every position is equally likely to hold any given card. There is nothing special about the last slot, the 40th slot, or any slot. Last card a spade. By symmetry the last position is just as likely to hold each of the 52 cards as the first position is. There are 13 spades among 52 cards, so P(	ext{last card is a spade}) = \frac{13}{52} = \frac{1}{4}. You do not need to reason about what came before; the identity of the final card is a uniform draw from the deck. 40th card is the ace of spades. Each specific card lands in each specific …

The color of the last card

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