Problem 34P

The second Earl of Yarborough is reported to have bet at odds of 1000 to 1 that a bridge hand of 13 cards would contain at least one card that is ten or higher. (By ten or higher we mean that a card is either a ten, a jack, a queen, a king, or an ace.) Nowadays, we call a hand that has no cards higher than 9 a Yarborough. What is the probability that a randomly selected bridge hand is a Yarborough?

Solution:

Step 1 of 2:

It is given that bridge hand of 13 cards contains at least one card that is ten or higher.

Also it is given that Yarborough is the hand that has no cards higher than 9.

Using this we need to find the probability that a randomly selected bridge hand is a Yarborough.