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The question is asking to compute the expected frequency for the marked cell (indicated with a "*") under the assumption of no association.

To calculate the expected frequency in a contingency table, under the assumption of no association (i.e., independence), we use the following formula:

\[
E_{ij} = \frac{(Row \, total \, for \, i) \times (Column \, total \, for \, j)}{Grand \, Total}
\]

Here’s the breakdown of the table:
- The marked cell is in row "Female" and column "B".
- The row total for females is 561 (since 1000 - 439 = 561).
- The column total for "B" is not provided directly, but we can calculate it by subtracting the other column totals from 1000.
- The grand total is 1000.

### Step-by-step:
1. **Total for column B**: 
   We have totals for columns A (231) and C (48), so column B total is:
   \[
   1000 - 231 - 48 = 721
   \]

2. **Row total for Female**: 
   \[
   1000 - 439 = 561
   \]

3. **Expected frequency for cell (Female, B)**: 
   \[
   E_{Female, B} = \frac{(Row \, total \, for \, Female) \times (Column \, total \, for \, B)}{Grand \, Total}
   \]
   \[
   E_{Female, B} = \frac{561 \times 721}{1000} = 404.481
   \]

Thus, the expected frequency for the marked cell is approximately **404.48**.

Would you like any more details or further clarification?

Here are 5 related questions you may want to explore:
1. How do you calculate expected frequencies in a contingency table?
2. What assumptions are made in chi-square tests of independence?
3. How do you calculate the chi-square statistic from observed and expected frequencies?
4. What is the interpretation of expected frequencies in the context of no association?
5. How can you test whether two variables are independent?

**Tip**: When calculating expected frequencies, always ensure you have both row and column totals, and use the grand total to find the expected value under the independence assumption.

Compute the expected frequency for the marked cell under the assumption of no association.

Learn how to compute the expected frequency for a marked cell in a contingency table under the assumption of no association. This involves key statistical concepts like contingency tables, independence assumptions, and the chi-square test. Suitable for Grades 10-12.

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