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Chapter 2: Q. 2.4 (page 52)

Calculate the number of possible five-card poker hands, dealt from a deck of 52 cards. (The order of cards in a hand does not matter.) A royal flush consists of the five highest-ranking cards (ace, king, queen, jack, 10) of any one of the four suits. What is the probability of being dealt a royal flush (on the first deal)?

Short Answer

Expert verified

The chances of getting a royal flush on the first deal are slim Pflushes=1.539脳10鈭�6

Step by step solution

01

Step1:definition of probability

Probability is a measure of the likelihood of an event occurring. Many events are impossible to predict with 100% accuracy. We can only predict the likelihood of an event occurring using it, that is, how likely it is to occur. Probability can range between zero and one, with zero indicating an impossible event and one indicating a certain event.

02

Step2:Probability of royal flushes

Because there are52 cards in the deck, the number of ways to choose five cards from this deck is:

惟(52,5)=52!5!(52鈭�5)!=2598960

There are four royal flushes among these ways, so the probability of these flushes is:

Pflushes=42598960=1.539脳10鈭�6

Pflushes=1.539脳10鈭�6

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Most popular questions from this chapter

Use Stirling's approximation to find an approximate formula for the multiplicity of a two-state paramagnet. Simplify this formula in the limit N鈫�鈮�Nto obtain 惟鈮�Ne/N鈫�N鈫�. This result should look very similar to your answer to Problem 2.17; explain why these two systems, in the limits considered, are essentially the same.

Consider an ideal monatomic gas that lives in a two-dimensional universe ("flatland"), occupying an area Ainstead of a volume V. By following the same logic as above, find a formula for the multiplicity of this gas, analogous to equation 2.40.

Show that during the quasistatic isothermal expansion of a monatomic ideal gas, the change in entropy is related to the heat input Qby the simple formula

鈭�s=QT

In the following chapter I'll prove that this formula is valid for any quasistatic process. Show, however, that it is not valid for the free expansion process described above.

Fill in the algebraic steps to derive the Sackur-Tetrode equation(2.49).

Use the methods of this section to derive a formula, similar to equation2.21, for the multiplicity of an Einstein solid in the "low-temperature" limit,q鈮�N .
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