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Chapter 2: Q. 2.34 (page 50)

The second Earl of Yarborough is reported to have bet at odds 1000-1that a bridge hand of13 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 than9 a Yarborough. What is the probability that a randomly selected bridge hand is a Yarborough?

Short Answer

Expert verified

There is approximately1in1800or 0.0547%chance that a bridge hand does not contain any card that is 10or higher.

Step by step solution

01

Given Information.

The second Earl of Yarborough is reported to have bet at odds1000-1that a bridge hand of 13cards would contain at least one card that is ten or higher.

02

Explanation.

If the dealing was fair, all5213hands are equally likely.

This is the number of combinations of 13out of 52different cards.

By the axioms of probability, the probability of an event Athat happens in nout of these5213hands is:

P(A)=n5213

In this case:

There are8lower in values in cards than 10. Accounting for suits 8路4=32cards from which to choose to create a hand that does not contain a 10or higher valued card -3213possible hands.

P(A)=32135213=5.47033路10-4

03

Explanation.

There is approximately 1in1800or 0.0547%chance that a bridge hand does not contain any card that is 10or higher.

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