The tenth card off the deck

Question

A shuffled deck has 20 cards, of which 4 are kings and 16 are not. Cards are dealt off the top one at a time. What is the probability that the tenth card dealt is a king?

Accepted Answer

A shuffle makes every ordering of the 20 cards equally likely. So the card sitting in the tenth position is a uniformly random card out of all 20, no different in its chances from the top card or the bottom card. Therefore the chance the tenth card is a king is just the king fraction: P(	ext{10th is a king})=\frac{4}{20}=\frac{1}{5}=0.2. Takeaway. In a fair shuffle, position carries no information before you look. The probability that any named position holds a king equals the fraction of kings in the deck.

The tenth card off the deck

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