Get a better hand

Discrete Mathematics Level pending

You are playing a game of poker, and you are dealt the following hand of cards from a shuffled standard poker deck:

\[\text{A}\spadesuit, \text{A}\clubsuit, \text{A}\color{red}{\heartsuit}, 6\color{red}{\heartsuit}, 10\color{red}{\diamondsuit}\]

You put the \(6\color{red}{\heartsuit}\) and \(10\color{red}{\diamondsuit}\) cards aside, and request to be dealt two new cards.

What is the probability that you will improve your hand to a Four of a Kind or a Full House?

Round your answer to three decimal places.

Note: Cards dealt to you are no longer in the deck. The \(6\color{red}{\heartsuit}\) and \(10\color{red}{\diamondsuit}\) cards are put aside; they are not put back into the deck.


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