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 $1,098,240$ $1,302,540$ $2,598,960$

Solution

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 \(\boxed{0.004165}\).

From Solvely APP
Source: https://solvelyapp.com/problems/FzBWNU5oql/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download