In the card game Bridge (and its predecessor Whist), a cooloquial term often used for a very bad hand is called a Yarborough. It is defined as any hand of 13 cards with no card greater than a 9 (i.e. no 10's, Jacks, Queens, Kings, or Aces). If a standard deck of 52 cards is dealt randomly to four players in a game of Bridge, what is the probability of:

(1) One player being dealt a Yarborough

(2) Two players being dealt a Yarborough

Guest Jul 30, 2021

#1**0 **

**Solutions:**

(1) Calculate the total number of 13-card hands when face-cards, aces, and tens are removed.

Divide this by the total number of 13-card hands from the complete deck

nCr(32, 13) / nCr(52, 13) = 0.0005470333581834

**This corresponds to odds of about (1) in (1829) hands**.

(2) **This is a conditional probability.** Given that one player has a Yarborough, what is the probability that a second player also has a Yarborough?

Calculate the total number of 13-card hands after an additional 13 cards are removed from the reduced deck. Divide this by the total number of 13-card hands from the complete deck.

nCr(32, 13) / nCr(52, 13) = 0.0000000427266467.

**The over all probability of two players being dealt a Yarborough** **in a single round** is

(0.0005470333581834) * (0.0000000427266467) = 0.00000000002337290102821668560478

**This corresponds to odds of about (1) in (42 784 590 531) rounds**,

GA

Guest Jul 31, 2021