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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=1.539×10−6

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:

Ω(52,5)=52!5!(52−5)!=2598960

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

Pflushes=42598960=1.539×10−6

Pflushes=1.539×10−6

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Most popular questions from this chapter

Suppose you flip 50fair coins.

(a) How many possible outcomes (microstates) are there?

(b) How many ways are there of getting exactly25heads and25tails?

(c) What is the probability of getting exactly 25heads and 25tails?

(d) What is the probability of getting exactly 30heads and 20tails?

(e) What is the probability of getting exactly 40heads and 10 tails?

(f) What is the probability of getting 50heads and no tails?

(g) Plot a graph of the probability of getting n heads, as a function of n.

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

Consider a system of two Einstein solids, Aand B, each containing 10 oscillators, sharing a total of 20units of energy. Assume that the solids are weakly coupled, and that the total energy is fixed.

(a) How many different macro states are available to this system?

(b) How many different microstates are available to this system?

(c) Assuming that this system is in thermal equilibrium, what is the probability of finding all the energy in solid A?

(d) What is the probability of finding exactly half of the energy in solid A?

(e) Under what circumstances would this system exhibit irreversible behavior?

For either a monatomic ideal gas or a high-temperature Einstein solid, the entropy is given by times some logarithm. The logarithm is never large, so if all you want is an order-of-magnitude estimate, you can neglect it and just say . That is, the entropy in fundamental units is of the order of the number of particles in the system. This conclusion turns out to be true for most systems (with some important exceptions at low temperatures where the particles are behaving in an orderly way). So just for fun, make a very rough estimate of the entropy of each of the following: this book (a kilogram of carbon compounds); a moose of water ; the sun of ionized hydrogen .

Use a pocket calculator to check the accuracy of Stirling's approximation forN=50 . Also check the accuracy of equation 2.16forlnN! .
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