in a 2-card hand, what is the probability of holding only face cards?

Well, let me consult with the royal family of playing cards for this one. Ah, yes. According to the King of Hearts, the Queen of Spades, and the Joker, there are a total of 12 face cards in a standard deck. So, if you're dealing a 2-card hand, there are 12 face cards out of a total of 52 cards. Therefore, the probability of holding only face cards in a 2-card hand is... 12 out of 52, which simplifies to 3 out of 13. So, it looks like your odds are just a bit over one in four, or as we say in the clown community, a "fairly facey" chance!

To calculate the probability of holding only face cards in a 2-card hand, we need to determine the total number of possible 2-card hands and the number of 2-card hands that consist only of face cards.

Step 1: Total number of 2-card hands
In a standard deck of 52 playing cards, there are C(52, 2) ways to choose 2 cards, which is equal to 52! / (2! * (52 - 2)!) = 1,326 possible 2-card hands.

Step 2: Number of 2-card hands with only face cards
There are 3 face cards in each of the four suits, giving us a total of 12 face cards in the deck (Jacks, Queens, and Kings). To calculate the number of 2-card hands with only face cards, we multiply the number of ways to choose 2 face cards (C(12, 2)) by C(40, 0), which represents choosing zero non-face cards. This simplifies to 12! / (2! * (12 - 2)!) * 1 = 66.

Step 3: Calculate the probability
Finally, we divide the number of 2-card hands with only face cards by the total number of 2-card hands:
Probability = Number of 2-card hands with only face cards / Total number of 2-card hands
Probability = 66 / 1326
Probability = 1 / 21

Therefore, the probability of holding only face cards in a 2-card hand is 1/21 or approximately 0.0476 (rounded to four decimal places).

To calculate the probability of holding only face cards in a 2-card hand, we need to determine the total number of possible 2-card hands and the number of those hands that consist of only face cards.

First, let's determine the total number of possible 2-card hands. There are 52 cards in a standard deck, so the number of ways to choose 2 cards out of 52 is given by the combination formula (nCr), where n is the total number of items and r is the number of items being chosen:

52C2 = 52! / (2! * (52-2)!) = 1326

Next, we need to determine the number of 2-card hands that consist of only face cards. In a standard deck of 52 cards, there are 12 face cards (Jack, Queen, King) since each of the four suits (Hearts, Diamonds, Clubs, Spades) has 3 face cards. To calculate the number of ways to choose 2 face cards out of 12, we can again use the combination formula:

12C2 = 12! / (2! * (12-2)!) = 66

Finally, we can calculate the probability by dividing the number of hands with only face cards by the total number of possible 2-card hands:

Probability = Number of hands with only face cards / Total number of possible 2-card hands

Probability = 66 / 1326 ≈ 0.0496 or approximately 4.96%

Therefore, the probability of holding only face cards in a 2-card hand is approximately 4.96%.

there are 12 face cards , ( J , Q, K 4 each)

so prob that for 2 cards, both cards are face
= C(12,2)/C(52,2) = 66/1326 = 11/221