# What is the probability that the last card is king if we are dealt $13$ cards from a well-shuffled desk?

A player is randomly dealt 13 cards from a standard, well-shuffled 52-card deck. What is the probability the 13th card dealt is a king?

• Do you know the probability that the first card is a king? Sep 13, 2016 at 9:18
• How about if you immediately took the 13th card - can you see that it is equally likely to be any card from the pack?
– Cato
Sep 13, 2016 at 9:41

## Hint

The 13th card you drew might as well have been the only card you drew. The other cards didn't even factor into it. Do you see why?

Now what is the probability that if you draw 1 card from the deck, it is a king?

• I think I don't understand your argument. Sep 13, 2016 at 9:24
• @ndakostan Can you pinpoint where you are stuck? Which part do you not follow? It was a hint, not a complete argument.
– 6005
Sep 13, 2016 at 9:25
• I am stuck in your saying that "The 13th card you drew might as well have been the only card you drew. The other cards didn't even factor into it". Can you explain more? Thank you very much. Sep 13, 2016 at 9:28
• @ndakostan Sure. As I am dealt the 13 cards, I could just set aside the first 12 face down, and then only look at the 13th card and not look at the first 13, and that would be equivalent. And the 13th card is random from the deck just like the 1st card is random from the deck.
– 6005
Sep 13, 2016 at 9:30
• I see it. But do you mean "not look at the first 12" or " not look at the first 13". Sep 13, 2016 at 9:33