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Problem Analysis and Solution

The image contains two sections: one involving a spinner and the other involving dice and an array of shapes. Let's solve each part step by step.

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#### Section 1: Spinner Problems

The spinner is divided into 8 equal sections, with different colors/shapes in each section. From the image:
- Gray pieces: 3 sections
- Black pieces: 2 sections
- White pieces: 3 sections

#### 1) How many pieces are there total in the spinner?
- The spinner is divided into 8 equal sections.
- Answer: 8

#### 2) If you spun the spinner 1 time, what is the probability it would land on a gray piece?
- There are 3 gray sections out of 8 total sections.
- Probability = (Number of gray sections) / (Total number of sections)
- Probability = \( \frac{3}{8} \)
- Answer: \( \frac{3}{8} \)

#### 3) If you spun the spinner 1 time, what is the probability it would land on a black piece?
- There are 2 black sections out of 8 total sections.
- Probability = (Number of black sections) / (Total number of sections)
- Probability = \( \frac{2}{8} = \frac{1}{4} \)
- Answer: \( \frac{1}{4} \)

#### 4) If you spun the spinner 1 time, what is the probability it would land on a white piece?
- There are 3 white sections out of 8 total sections.
- Probability = (Number of white sections) / (Total number of sections)
- Probability = \( \frac{3}{8} \)
- Answer: \( \frac{3}{8} \)

#### 5) If you spun the spinner 1 time, what is the probability of landing on either a white piece or a black piece?
- Number of white sections = 3
- Number of black sections = 2
- Total favorable sections = 3 (white) + 2 (black) = 5
- Probability = (Number of favorable sections) / (Total number of sections)
- Probability = \( \frac{5}{8} \)
- Answer: \( \frac{5}{8} \)

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#### Section 2: Dice Problems

A standard die has 6 faces, numbered 1 through 6.

#### 6) If you were to roll the die one time, what is the probability it will land on a 3?
- There is 1 face with the number 3.
- Total number of faces = 6
- Probability = (Number of favorable outcomes) / (Total number of outcomes)
- Probability = \( \frac{1}{6} \)
- Answer: \( \frac{1}{6} \)

#### 7) If you were to roll the die one time, what is the probability it will NOT land on a 2?
- There is 1 face with the number 2.
- Number of faces that are NOT 2 = 6 - 1 = 5
- Probability = (Number of favorable outcomes) / (Total number of outcomes)
- Probability = \( \frac{5}{6} \)
- Answer: \( \frac{5}{6} \)

#### 8) If you were to roll the die one time, what is the probability of it landing on an even number?
- Even numbers on a die: 2, 4, 6 (3 numbers)
- Total number of faces = 6
- Probability = (Number of favorable outcomes) / (Total number of outcomes)
- Probability = \( \frac{3}{6} = \frac{1}{2} \)
- Answer: \( \frac{1}{2} \)

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#### Section 3: Array Problems

The array consists of 25 shapes in total. From the image:
- Circles: 8 shapes
- Squares: 9 shapes
- Hearts: 6 shapes
- Diamonds: 2 shapes

#### 9) How many shapes are there total in the array?
- Counting all the shapes: 8 (circles) + 9 (squares) + 6 (hearts) + 2 (diamonds) = 25
- Answer: 25

#### 10) If you were to select 1 shape at random from the array, what is the probability it will be a circle?
- Number of circles = 8
- Total number of shapes = 25
- Probability = (Number of circles) / (Total number of shapes)
- Probability = \( \frac{8}{25} \)
- Answer: \( \frac{8}{25} \)

#### 11) If you were to select 1 shape at random from the array, what shape do you have the greatest probability of selecting?
- Circles: 8 shapes
- Squares: 9 shapes
- Hearts: 6 shapes
- Diamonds: 2 shapes
- The shape with the greatest number of occurrences is squares (9 shapes).
- Answer: Squares

#### 12) Which shape has a 32% chance (8 out of 25) of being selected?
- A 32% chance corresponds to \( \frac{8}{25} \).
- From the counts, circles have 8 shapes out of 25.
- Answer: Circles

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Final Answers:

1. \( \boxed{8} \)
2. \( \boxed{\frac{3}{8}} \)
3. \( \boxed{\frac{1}{4}} \)
4. \( \boxed{\frac{3}{8}} \)
5. \( \boxed{\frac{5}{8}} \)
6. \( \boxed{\frac{1}{6}} \)
7. \( \boxed{\frac{5}{6}} \)
8. \( \boxed{\frac{1}{2}} \)
9. \( \boxed{25} \)
10. \( \boxed{\frac{8}{25}} \)
11. \( \boxed{\text{Squares}} \)
12. \( \boxed{\text{Circles}} \)