In 5​-card ​poker, played with a standard​ 52-card deck, 52C5​, or 2,598,960​, different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 2,598,960. Shown to the right is the number of ways a particular type of hand can occur and its associated probability. Find the probability of not being dealt this type of hand.

To find the probability of *not* being dealt a particular type of hand in 5-card poker, we can use the following approach:

1. The probability of being dealt a specific type of hand is given as:
   \[
   P(\text{dealt}) = \frac{\text{number of ways the hand can occur}}{2,598,960}
   \]

2. The probability of **not** being dealt that hand is simply the complement of this probability:
   \[
   P(\text{not dealt}) = 1 - P(\text{dealt})
   \]
   or
   \[
   P(\text{not dealt}) = 1 - \frac{\text{number of ways the hand can occur}}{2,598,960}
   \]

If you have the number of ways a particular hand can occur, I can help you calculate the exact probability.

### Example:
If the number of ways the hand can occur is, say, 4,000, then:
\[
P(\text{dealt}) = \frac{4000}{2,598,960} \approx 0.00154
\]
And the probability of **not** being dealt that hand is:
\[
P(\text{not dealt}) = 1 - 0.00154 = 0.99846
\]

Please provide the specific number of ways, and I will calculate the exact probability for you.

---

Would you like to provide that number or have more details? 

Here are 5 related questions to consider:
1. What is the probability of being dealt a royal flush?
2. How many different types of poker hands are there?
3. What is the most common type of hand in poker?
4. How does the deck size affect poker probabilities?
5. What is the probability of being dealt two pairs in a 5-card poker hand?

**Tip:** In probability, the complement rule is a useful shortcut: \( P(\text{not A}) = 1 - P(\text{A}) \).

In 5-card poker, played with a standard 52-card deck, 52C5, or 2,598,960 different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 2,598,960. Shown to the right is the number of ways a particular type of hand can occur and its associated probability. Find the probability of not being dealt this type of hand.

Explore how to calculate the probability of not being dealt a specific hand in 5-card poker. Using combinatorics and probability, this solution demonstrates the complement rule to find the chance of not getting a particular hand. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation