Problem

In 5-card poker, the number of outcomes favorable to an event $E$ is given in the table. Find the probability of being dealt four of a kind or a a straight.

The probability of being dealt four of a kind or a straight is $\square$.
(Round to 6 decimal places.)
Event $\mathrm{E}$
Royal flush
Straight flush
Four of a kind
Full house
Flush
Straight
Three of a kind
Two pairs
One pair
No pair
Total
\# of Outcomes Favorable to E
4
36
624
3744
5108
10,200
54,912
123,552
$1,098,240$
$1,302,540$
$2,598,960$

Answer

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Answer

Final Answer: The probability of being dealt four of a kind or a straight in a 5-card poker game is approximately \(\boxed{0.004165}\).

Steps

Step 1 :The problem is asking for the probability of being dealt four of a kind or a straight in a 5-card poker game.

Step 2 :To find this, we need to add the number of outcomes favorable to four of a kind and a straight, and then divide by the total number of outcomes.

Step 3 :The total number of outcomes is given as 2,598,960.

Step 4 :The number of outcomes favorable to four of a kind is given as 624 and the number of outcomes favorable to a straight is given as 10,200.

Step 5 :So, the probability is calculated as follows: \( \frac{{624 + 10,200}}{{2,598,960}} \).

Step 6 :Performing the calculation gives a probability of approximately 0.004165.

Step 7 :Final Answer: The probability of being dealt four of a kind or a straight in a 5-card poker game is approximately \(\boxed{0.004165}\).

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