Probability worksheet with a bag of numbered tiles and questions on likelihood of picking certain numbers.

To solve the probability problems, we need to analyze the numbers in the bag and determine the likelihood of each event. The numbers in the bag are:

\[ 3, 6, 9, 7, 4, 1, 8, 5, 2 \]

There are a total of 9 tiles in the bag.

Step-by-Step Solution:

#### 1. Picking 1
- Favorable outcomes: \( \{1\} \) (only one tile is labeled "1")
- Total possible outcomes: 9
- Probability:
\[
P(\text{picking 1}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{9}
\]

#### 2. Picking 3 or 5
- Favorable outcomes: \( \{3, 5\} \) (two tiles are labeled "3" and "5")
- Total possible outcomes: 9
- Probability:
\[
P(\text{picking 3 or 5}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{9}
\]

#### 3. Picking 77
- Favorable outcomes: \( \{\} \) (there is no tile labeled "77")
- Total possible outcomes: 9
- Probability:
\[
P(\text{picking 77}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{0}{9} = 0
\]

#### 4. Picking odd numbers
- Odd numbers in the bag: \( \{3, 1, 7, 5\} \) (four tiles are odd: 3, 1, 7, 5)
- Total possible outcomes: 9
- Probability:
\[
P(\text{picking odd numbers}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{9}
\]

#### 5. Picking a multiple of 3
- Multiples of 3 in the bag: \( \{3, 6, 9\} \) (three tiles are multiples of 3: 3, 6, 9)
- Total possible outcomes: 9
- Probability:
\[
P(\text{picking a multiple of 3}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{9} = \frac{1}{3}
\]

#### 6. Picking a number greater than 4
- Numbers greater than 4 in the bag: \( \{6, 7, 5, 8, 9\} \) (five tiles are greater than 4: 6, 7, 5, 8, 9)
- Total possible outcomes: 9
- Probability:
\[
P(\text{picking a number greater than 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{5}{9}
\]

#### 7. Picking 0
- Favorable outcomes: \( \{\} \) (there is no tile labeled "0")
- Total possible outcomes: 9
- Probability:
\[
P(\text{picking 0}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{0}{9} = 0
\]

#### 8. Picking a number greater than 4
- This is the same as question 6.
- Numbers greater than 4 in the bag: \( \{6, 7, 5, 8, 9\} \) (five tiles are greater than 4: 6, 7, 5, 8, 9)
- Total possible outcomes: 9
- Probability:
\[
P(\text{picking a number greater than 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{5}{9}
\]

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Picking 1:} & \frac{1}{9} \\
\text{Picking 3 or 5:} & \frac{2}{9} \\
\text{Picking 77:} & 0 \\
\text{Picking odd numbers:} & \frac{4}{9} \\
\text{Picking a multiple of 3:} & \frac{1}{3} \\
\text{Picking a number greater than 4:} & \frac{5}{9} \\
\text{Picking 0:} & 0 \\
\text{Picking a number greater than 4:} & \frac{5}{9} \\
\end{array}
}
\]