0
$\begingroup$

A group of 4 friends are playing a card game using a standard deck of 52 cards. Each friend receives one card from the deck, and the next card is flipped up. Only one of the friend has a card that matches the suit of the flipped up card. What is the probability that only one person is able to have a suit that matches the suit of the card that's flipped up?

My work (it's most likely wrong):

Let's say that the turned up card is a hearts. There are 13 hearts in a deck of hearts.

13*39*38*37= 712,842

Only one of the cards is a hearts (13). The rest of the cards are not hearts (39, 38, 37).

The probability that one player has the matching suit -> 13/712,842.

The number is too small, and I feel that I did something wrong.

$\endgroup$
1
$\begingroup$

Three things:

  1. With the card being flipped one of the $13$ hearts, the player whose card is a heart as well must have one of the $12$ remaining hearts, not $13$. So you must use a factor of $12$ not $13$

  2. There are $4$ possible players whose card is a heart, so you need to have a factor of $4$ in there.

  3. Most importantly, you should not be dividing by the factors of $12$, $39$, $38$, and $37$: these are the possible target combinations that go in the numerator. The denominator are all the possible ways to get $4$ cards to the $4$ players, so there you get something like $51$, $50$, $49$, and $48$

OK, using these hints, try again!

$\endgroup$
  • $\begingroup$ @N.F.Taussig Right, thanks! :P $\endgroup$ – Bram28 Dec 3 '18 at 12:22
  • $\begingroup$ Since one card is placed on the table, there are $51$ cards left from which the four players can each select a card. $\endgroup$ – N. F. Taussig Dec 3 '18 at 12:27
  • $\begingroup$ Thanks! Would it be instead 51, 50, 49, and 48 since one of the cards is already used up? $\endgroup$ – Lauren Pablo Dec 3 '18 at 12:28
  • $\begingroup$ @laurenpablo exactly! $\endgroup$ – Bram28 Dec 3 '18 at 13:01

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.