Two Aces?

Three playing cards, two Aces and a King, are on the table upside down.

One of the three is then returned to the deck, leaving only two cards on the table.

  • Ryan picks one of the two at random. It's an Ace.
  • Maya picks one of the two at random. It's an Ace.
  • Hana picks one of the two at random. It's an Ace.
  • Jaycie picks one of the two at random. It's an Ace.

If the probability that both cards are Aces is \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is \(a+b\)?


Image credit: http://www.goodpokergames.com
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