Problem
Poker is a common game in which players are dealt five cards from a deck of cards. It can be shown that there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in the table below. Find the requested probability. Use a calculator. (Show your answer to nine decimal places.) \[ P(\text { straight) } \] 2598960 Poker Hands Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3,744 hands Flush 5,108 hands Straight 10,200 hands Three of a kind 54,912 hands Two pair 123,552 hands One pair $1,098,240$ hands *All of these probabilities are mutually exclusive. That is, the 36 straight flushes do not include the 4 royal flushes, and the 5,108 flush hands do not include the better hands of straiaht flush or roval flush.
Solution
Step 1 ：The problem is asking for the probability of getting a straight in a poker game. To calculate this, we need to divide the number of ways to get a straight by the total number of possible poker hands.
Step 2 ：The total number of possible poker hands is given as 2,598,960.
Step 3 ：The number of ways to get a straight is given as 10,200.
Step 4 ：So, we need to divide 10,200 by 2,598,960 to get the probability.
Step 5 ：\(\frac{10200}{2598960} = 0.003924646781789639\)
Step 6 ：Final Answer: The probability of getting a straight in a poker game is approximately \(\boxed{0.003924646}\).
