1
$\begingroup$

We have a "French playing cards" composed of $52$ cards. Each kind of cards (Ace, King, Queen, ...) is composed of $4$ cards : There are $4$ Ace, $4$ Jack, etc. We pull $5$ cards among the $52$ cards.

We are a four (of a kind) if among the $5$ cards pulled, there are the $4$ of a same value ($4$ cards Ace, or King, or 2, or 3......).

enter image description here

What is the probability to have a four (of a kind) if the first card pulled is an Ace, and the fifth card pulled is a King ?

I hope you understand, it's very difficult for me to translate that. Thank you for help in advance.

$\endgroup$
3
  • $\begingroup$ In English, As is Ace, Valet is Jack or Knave, Dame is Queen and Roi is King. $\endgroup$ Jan 25, 2018 at 20:20
  • $\begingroup$ Thank you, I edit immediately ! $\endgroup$ Jan 25, 2018 at 20:25
  • $\begingroup$ Some more English terminology: For the four of hearts (quatre coeurs?), the four is called the rank of the card, and hearts is called the suit of the card. $\endgroup$
    – John
    Jan 25, 2018 at 20:27

1 Answer 1

1
$\begingroup$

Here is a hint:

Given that you have drawn one ace and one king, you will need either to draw the remaining three aces, or draw the remaining three kings, from the remaining $50$ cards.

Can you continue from this point?

(Spoiler answer)

There are two winning ways to draw the remaining three cards, and ${50 \choose 3}$ total ways to draw the remaining three cards, so the probability is $2/{50 \choose 3}$.

$\endgroup$
1

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.