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The symbol you're referring to in the image is a **probability** symbol. The notation \( \mathbb{P}(A / H) = 1 \) represents a **conditional probability**, where the probability of event \( A \), given that \( H \) has occurred, is 1.

Here is the breakdown of the expression:

- \( A \supseteq H \): This symbol \( \supseteq \) means that \( A \) is a **superset** of \( H \), meaning \( A \) contains \( H \) or all elements of \( H \) are also in \( A \).
- \( \mathbb{P}(A / H) = 1 \): The conditional probability that \( A \) happens, given that \( H \) has happened, is equal to 1. This means that if \( H \) happens, \( A \) must always happen.

The key takeaway is that \( A \) includes all possible outcomes of \( H \), so knowing \( H \) has occurred guarantees that \( A \) will also occur.

Would you like further details or clarification?

Here are five related questions for further exploration:
1. What is the difference between conditional probability and regular probability?
2. How do you interpret conditional probability when \( \mathbb{P}(A / H) = 0 \)?
3. What does it mean if \( A \subseteq H \) instead of \( A \supseteq H \)?
4. How does Bayes' theorem apply to conditional probabilities like this?
5. Can you explain the significance of events having probability 1 in probability theory?

**Tip**: When working with conditional probability, always check if the conditions ensure that the given event is certain or impossible!

Understand the relationship between conditional probability and set theory. This problem explains the concept of a superset (A ⊇ H) and how it guarantees that ℙ(A/H) = 1. Ideal for students learning probability and set theory at the undergraduate level.

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