To express the event "The red die shows 6 and the numbers add to 9" in symbolic form, we can combine the given events $A$ and $B$ with the logical "and" operation, which is denoted by $\cap$. So we have:

$A \cap B$

This event represents the situation where both the red die shows a 6, and the sum of the numbers on both dice is 9.

Finding the Number of Elements in $A \cap B$

For $A \cap B$ to occur:

1. The red die (showing 6) restricts the red die’s outcome to 6.
2. The sum must be 9, so the green die must show 3 (since $6 + 3 = 9$).

Therefore, the only outcome satisfying $A \cap B$ is:

• Red die shows 6, and green die shows 3.

Since there is only one possible outcome for this event, $A \cap B$ contains exactly 1 element.

Would you like more details or have any questions about this solution?

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Here are some related questions to expand your understanding:

1. How would you express "The red die shows 6 or the numbers add to 9" in symbolic form?
2. What would be the symbolic form for the event "At least one of the dice shows 6 and the numbers do not add to 9"?
3. How many outcomes are there for the event where both dice show the same number?
4. If we want the sum of the dice to be even, what are the possible outcomes?
5. What is the probability of getting a sum of 9 when rolling two dice?

Tip: When analyzing events with multiple conditions, identify which values satisfy each condition individually before combining them.