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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

According to the Sackur-Tetrode equation, the entropy of a monatomic ideal gas can become negative when its temperature (and hence its energy) is sufficiently low. Of course this is absurd, so the Sackur-Tetrode equation must be invalid at very low temperatures. Suppose you start with a sample of helium at room temperature and atmospheric pressure, then lower the temperature holding the density fixed. Pretend that the helium remains a gas and does not liquefy. Below what temperature would the Sackur-Tetrode equation predict that Sis negative? (The behavior of gases at very low temperatures is the main subject of Chapter 7.)

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(d) Derive the useful approximation

localid="1650331649052" ln鈦�(1+x)鈮�x

which is valid when localid="1650331651790" |x|鈮�1. Use a calculator to check the accuracy of this approximation for localid="1650331654235" x=0.1and localid="1650331656447" x=0.01.

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