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We are working with a deck of cards numbered from 1 to 8, and they are split into two groups based on color:
- Cards numbered 3, 4, 5, 6, 7, and 8 are grey.
- Cards numbered 1 and 2 are white.

### Definitions:
- Let \( X \) be the event that the drawn card is grey.
- Let \( \text{not } X \) be the event that the drawn card is **not grey** (i.e., the card is white).
  
We are asked to calculate probabilities for the following:
- \( P(X) \) (the probability that a card is grey).
- \( P(\text{not } X) \) (the probability that a card is not grey).
- \( 1 - P(\text{not } X) \).

#### Step 1: Identify outcomes
- Grey cards: 3, 4, 5, 6, 7, 8 → total of 6 grey cards.
- White cards: 1, 2 → total of 2 white cards.

#### Step 2: Calculate probabilities
- Total number of cards: 8 (cards numbered 1 to 8).
  
1. **\( P(X) \)**:
   \[
   P(X) = \frac{\text{Number of grey cards}}{\text{Total number of cards}} = \frac{6}{8} = 0.75
   \]

2. **\( P(\text{not } X) \)**:
   \[
   P(\text{not } X) = \frac{\text{Number of white cards}}{\text{Total number of cards}} = \frac{2}{8} = 0.25
   \]

3. **\( 1 - P(\text{not } X) \)**:
   \[
   1 - P(\text{not } X) = 1 - 0.25 = 0.75
   \]

### Table Completion:
- For \( X \), mark the boxes corresponding to cards numbered 3 to 8.
- For \( \text{not } X \), mark the boxes corresponding to cards numbered 1 and 2.
- For the probabilities:
  - \( P(X) = 0.75 \)
  - \( P(\text{not } X) = 0.25 \)
  - \( 1 - P(\text{not } X) = 0.75 \)

Would you like further clarification or additional details?

### Related questions:
1. What is the probability of drawing a card numbered 7 or 8?
2. If two cards are drawn randomly without replacement, what is the probability that both are grey?
3. How would the probabilities change if a card numbered 9 (also grey) was added to the deck?
4. What is the complement of the event \( X \), and how does it relate to \( P(\text{not } X) \)?
5. How would you represent this scenario using a Venn diagram?

**Tip:** Probabilities are often complements, so \( P(\text{not } X) = 1 - P(X) \). Use this relationship to check your work.

We have a deck of 8 cards numbered from 1 to 8. Some are grey, and some are white. Cards numbered 3 to 8 are grey, and cards numbered 1 and 2 are white. A card is drawn at random. We are asked to compute the probability of drawing a grey card (P(X)) and the probability of not drawing a grey card (P(not X)).

Learn how to calculate the probability of drawing a grey card from a deck of 8 cards where some are grey, and some are white. The problem covers basic probability concepts, using the complement rule to find P(X) and P(not X). Suitable for students in Grades 6-8.

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