Question

Find the probability of being dealt two kings and two fives when playing five card poker from a standard deck of fifty-two playing cards.Express your answer in the correct probability form. Use the dash symbols "/" or "\" for expressing the probability as a fraction.

Answer 1

The probability of being deal a card from a deck is the amount of cards in the deck that are equal to the one you are being dealt divided by the total cards in teh deck.

To find the probability of being dealt a king from a deck of 52 cards, Since there are 4 kings in the deck:

`P(King)=(4)/(52)=(1)/(13)`

Now, there is one less card in the deck, The total number of cards in the deck is 52 - 1 = 51. Now, in the deck there is one less king, then:

`\begin{gathered} P(Second\text{ }King)=(3)/(51)=(1)/(17) \\ \end{gathered}`

Next, the fives. Now in the deck there are 50 cards, and 4 fives:

`P(Five)=(4)/(50)=(2)/(25)`

And to get a second five, now there are 49 cards in the deck and 3 fives:

`P(Second\text{ }Five)=(3)/(49)`

All these events are independent. The previous and the next card dealt does not interfere in any with the others. To find the probability of those events all happening at the same time, we need to multiply:

`P(King)\cdot P(Second\text{ }King)\cdot P(Five)\cdot P(Second\text{ }Five)=(1)/(13)\cdot(1)/(17)\cdot(2)/(25)\cdot(3)/(49)=(6)/(270725)`

That's the probability:

`P=(6)/(270725)`