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Let's analyze and solve the questions step-by-step:

### Question 9.1.1: Completing the Table

We know:
- There are 8 fruit trees and 12 other trees, giving a total of \( 8 + 12 = 20 \) trees.
- There are 7 trees with birds nesting in them, out of which 3 are fruit trees.

Using this information, let's complete the table.

|                   | Fruit Trees | Other Trees | Total |
|-------------------|-------------|-------------|-------|
| Birds nest        | 3           | 4           | 7     |
| No birds nest     | 5           | 8           | 13    |
| Total             | 8           | 12          | 20    |

**Explanation**:
- Since there are 7 trees with birds nesting and 3 of them are fruit trees, the other 4 must be other trees.
- Since there are 8 fruit trees in total, \(8 - 3 = 5\) of them do not have birds nesting.
- Similarly, there are 12 other trees in total, so \(12 - 4 = 8\) do not have birds nesting.

### Question 9.1.2: Probability that a Climbable Fruit Tree Has Birds Nesting

Jayda climbs a fruit tree. We need to find the probability that this tree has birds nesting in it.

The probability \( P(\text{birds nest | fruit tree}) \) is calculated as:
\[
P(\text{birds nest | fruit tree}) = \frac{\text{Number of fruit trees with birds nesting}}{\text{Total number of fruit trees}} = \frac{3}{8}
\]

### Question 9.1.3: Probability Jayda Follows Instructions

Jayda has been told not to climb:
- Any fruit trees, or
- Any trees with birds nesting.

This means Jayda is allowed to climb trees that:
- Are "Other trees" (not fruit trees), and
- Do not have birds nesting.

From the table, we see that there are 8 such trees ("Other trees" with no birds nesting).

The probability \( P(\text{follows instructions}) \) is:
\[
P(\text{follows instructions}) = \frac{\text{Number of trees allowed to climb}}{\text{Total number of trees}} = \frac{8}{20} = \frac{2}{5}
\]

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Let me know if you would like further details on any of these steps or if you have questions about specific parts.

### Related Questions

1. What is the probability that a randomly chosen tree has birds nesting?
2. How many trees are in total and how does this impact the probabilities?
3. If Jayda chooses a tree at random, what is the chance it is a fruit tree?
4. Can we calculate the probability that a randomly chosen tree has no birds nesting?
5. How would the probability change if more birds nested in other trees?

### Tip
Remember to always check if an event has specific restrictions or conditions, as this affects how probabilities are calculated.

There are 8 fruit trees and 12 other trees in Mrs. Green’s garden. There are birds nesting in 7 of the trees, but only 3 of these trees are fruit trees. Complete the table and answer questions about probability related to the trees in the garden.

Solve probability questions based on tree and bird nesting data from Mrs. Green's garden. Learn how to calculate conditional probability and interpret data in tables. Suitable for students in Grades 8-10.

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