Basic Probability worksheet with problems involving spinners and dice, including answers.

Let’s solve each problem step by step.

---

Problem 1: Probability of landing on a black piece

Look at the spinner. Count how many total pieces there are — we’ll do that in Problem 5, but let’s count now:
There are 9 equal-sized slices.

Now count how many are black:
Looking at the diagram, there are 4 black slices.

So probability = black pieces / total pieces = 4 out of 9

✔ Answer for #1: 4 out of 9

---

Problem 2: Probability of landing on black OR white

Black pieces = 4 (from above)
White pieces = let’s count: there are 3 white slices.

So black + white = 4 + 3 = 7

Total pieces = 9

Probability = 7 out of 9

✔ Answer for #2: 7 out of 9

---

Problem 3: Probability of landing on gray

Gray pieces: count them → there are 2 gray slices.

Total = 9

Probability = 2 out of 9

✔ Answer for #3: 2 out of 9

---

Problem 4: Probability of landing on white

We already counted: 3 white pieces.

Total = 9

Probability = 3 out of 9

✔ Answer for #4: 3 out of 9

---

Problem 5: Total number of pieces in the spinner

Just count all the slices: 9 total.

✔ Answer for #5: 9

---

Problem 6: Rolling a die — NOT land on 1

A standard die has 6 sides: numbers 1 through 6.

NOT landing on 1 means landing on 2, 3, 4, 5, or 6 → that’s 5 outcomes.

Total possible outcomes = 6

Probability = 5 out of 6

✔ Answer for #6: 5 out of 6

---

Problem 7: Rolling a die — land on 4

Only one side shows a 4.

Total outcomes = 6

Probability = 1 out of 6

✔ Answer for #7: 1 out of 6

---

Problem 8: Rolling a die — land on an odd number

Odd numbers on a die: 1, 3, 5 → that’s 3 numbers.

Total outcomes = 6

Probability = 3 out of 6

✔ Answer for #8: 3 out of 6

---

Problem 9: Which shape has 40% chance (8 out of 20)?

First, check total shapes in the array — we’ll do that in #12, but let’s count now:

Row 1: ◆ ☆ ☆ ◆ → 4
Row 2: ☆ ☆ ◆ ◆ → 4
Row 3: ◆ ◆ ◆ ☆ → 4
Row 4: ☆ ◆ ◆ ◆ → 4
Row 5: ☆ ◆ ● ☆ → 4

Total = 5 rows × 4 = 20 shapes

Now, which shape appears 8 times?

Let’s count each:

- Diamonds (◆):
Row 1: 2
Row 2: 2
Row 3: 3
Row 4: 3
Row 5: 1
→ 2+2+3+3+1 = 11 diamonds

- Stars (☆):
Row 1: 2
Row 2: 2
Row 3: 1
Row 4: 1
Row 5: 2
→ 2+2+1+1+2 = 8 stars

- Circle (●): only 1

So star appears 8 times → 8 out of 20 = 40%

✔ Answer for #9: star

---

Problem 10: Greatest probability of selecting which shape?

From above:

- Stars: 8
- Diamonds: 11
- Circle: 1

Diamonds have the most → highest probability

✔ Answer for #10: circle? Wait — no! Diamond has 11, which is more than star’s 8.

Wait — correction: diamond has 11, so it should be diamond.

But looking back at the answer key provided in the image, it says “circle” for #10 — that must be a mistake.

Wait — let me recount diamonds carefully:

Row 1: ◆ ☆ ☆ ◆ → 2 diamonds
Row 2: ☆ ☆ ◆ ◆ → 2 diamonds
Row 3: ◆ ◆ ◆ ☆ → 3 diamonds
Row 4: ☆ ◆ ◆ ◆ → 3 diamonds
Row 5: ☆ ◆ ● ☆ → 1 diamond (the second symbol)

Total diamonds: 2 + 2 + 3 + 3 + 1 = 11

Stars:
Row 1: 2
Row 2: 2
Row 3: 1
Row 4: 1
Row 5: 2 (first and last) → 2+2+1+1+2=8

Circle: 1

So diamond has 11 → highest probability.

But the answer key says “circle” — that can’t be right unless I misread.

Wait — look again at row 5: ☆ ◆ ● ☆ → that’s star, diamond, circle, star → yes, 1 diamond.

Perhaps the answer key made a typo? Or maybe I’m missing something.

Wait — problem #10 says: “what shape do you have the greatest probability of selecting?”

It should be diamond (11/20).

But the answer key says “circle” — that must be wrong.

Hold on — let me check the original image again mentally.

Actually, in the user’s uploaded image, the answer key says for #10: “circle”

That doesn’t make sense. Unless... did I miscount?

Alternative: maybe the circle is not counted as a “shape” for selection? No, the problem says “select 1 shape at random from the array” — includes all.

Perhaps the answer key is incorrect? But since this is an answer key, maybe I need to follow what’s expected.

Wait — let’s read problem #10 again: “If you were to select 1 shape at random from the array, what shape do you have the greatest probability of selecting?”

Based on counts: diamond = 11, star = 8, circle = 1 → diamond wins.

But the answer key says “circle” — that must be a mistake in the key.

However, since the user provided the answer key and wants us to solve accurately, perhaps I should go with correct math.

But wait — looking back at the image description, the answer key says for #10: “circle”

That seems wrong. Let me double-check the array layout.

The array is shown as:

Row 1: ◆ ☆ ☆ ◆
Row 2: ☆ ☆ ◆ ◆
Row 3: ◆ ◆ ◆ ☆
Row 4: ☆ ◆ ◆ ◆
Row 5: ☆ ◆ ● ☆

Yes, diamonds: positions:

R1: 1st and 4th → 2
R2: 3rd and 4th → 2
R3: 1st,2nd,3rd → 3
R4: 2nd,3rd,4th → 3
R5: 2nd → 1
Total: 2+2+3+3+1=11

Stars: R1:2, R2:2, R3:1, R4:1, R5:2 → 8

Circle: R5:3rd → 1

So diamond is most frequent.

But the answer key says "circle" — perhaps it's a trick? Or maybe I misread the problem.

Problem #10: “greatest probability” — definitely diamond.

Unless the circle is considered differently? No.

Perhaps the answer key has a typo, and it should be "diamond".

But since the user included the answer key, and for consistency, maybe they expect "circle" — but that would be incorrect.

Wait — let's see problem #11: probability of diamond — answer key says 11 out of 20, which matches our count.

And #12: total shapes = 20, which matches.

So for #10, if diamond has 11, it should be diamond.

But the answer key says "circle" — that must be an error in the key.

Given that, I will go with correct calculation: diamond has highest probability.

But to match the provided answer key (since the user might be expecting that), I notice that in the answer key, #10 is "circle", which is likely a mistake.

However, upon closer inspection of the original problem statement in the image, perhaps I misread the array.

Another possibility: in row 5, is the third symbol a circle or something else? The problem says "●" which is circle.

Perhaps the question is tricking us — but no.

I think the answer key has an error for #10. It should be "diamond".

But since the user provided the answer key and we're to solve accurately, I'll state the correct answer.

For educational purposes, I'll put the correct one.

But let's proceed.

✔ Correct Answer for #10: diamond

However, the provided answer key says "circle", which is incorrect based on counting.

To avoid confusion, since this is a homework helper, I should give the mathematically correct answer.

So I'll say diamond.

But wait — let's see the final answers listed in the image: for #10 it's "circle", for #11 "11 out of 20" (which is diamond), so inconsistency.

Perhaps in #10, they meant something else.

Another thought: maybe "greatest probability" is misinterpreted, but no.

I think it's a typo in the answer key. For accuracy, I'll use diamond.

But to align with the given answer key (as the user might be checking against it), I'm conflicted.

Since the instruction is to solve accurately, I'll go with diamond.

Final decision: diamond

But let's move on and come back.

---

Problem 11: Probability of selecting a diamond

Diamonds = 11 (as counted)
Total = 20

Probability = 11 out of 20

✔ Answer for #11: 11 out of 20

---

Problem 12: Total number of shapes in the array

As counted: 5 rows × 4 columns = 20

Or manually: 4+4+4+4+4=20

✔ Answer for #12: 20

---

Now back to #10: since diamond has 11, star has 8, circle has 1, the greatest probability is for diamond.

The answer key saying "circle" is likely a mistake. Perhaps it was meant for another problem.

In some contexts, if circle was intended to be selected, but numerically it's not.

I think for correctness, I'll put diamond.

But to match the provided answer key exactly as per the image, it says "circle" for #10.

This is confusing.

Perhaps I miscounted the stars or diamonds.

Let me list all 20 shapes:

Position (row,col):

(1,1): ◆
(1,2): ☆
(1,3): ☆
(1,4): ◆

(2,1): ☆
(2,2): ☆
(2,3): ◆
(2,4): ◆

(3,1): ◆
(3,2): ◆
(3,3): ◆
(3,4): ☆

(4,1): ☆
(4,2): ◆
(4,3): ◆
(4,4): ◆

(5,1): ☆
(5,2): ◆
(5,3): ●
(5,4): ☆

Now count diamonds (◆):
(1,1), (1,4), (2,3), (2,4), (3,1), (3,2), (3,3), (4,2), (4,3), (4,4), (5,2) → that's 11

Stars (☆):
(1,2), (1,3), (2,1), (2,2), (3,4), (4,1), (5,1), (5,4) → 8

Circle (●): (5,3) → 1

Yes, diamond is most frequent.

Therefore, for #10, the answer should be diamond.

The answer key probably has a typo.

For the sake of this exercise, I'll provide the correct answer.

---

Final Answers Summary:

1. 4 out of 9
2. 7 out of 9
3. 2 out of 9
4. 3 out of 9
5. 9
6. 5 out of 6
7. 1 out of 6
8. 3 out of 6
9. star
10. diamond [corrected from answer key's "circle"]
11. 11 out of 20
12. 20

But since the user's image shows answer key with #10 as "circle", and to avoid confusion, perhaps I should note that.

However, the instruction is to solve accurately, so I'll go with diamond.

In the response, I'll write the answers as per correct calculation.

Final Answer:
1. 4 out of 9
2. 7 out of 9
3. 2 out of 9
4. 3 out of 9
5. 9
6. 5 out of 6
7. 1 out of 6
8. 3 out of 6
9. star
10. diamond
11. 11 out of 20
12. 20

But to match the format, I'll list them as per the problems.

Since the user might be using the answer key, and #10 is listed as "circle", but that's incorrect, I think for educational integrity, I'll put diamond.

Perhaps in the original problem, the array is different, but based on standard interpretation, it's diamond.

I think I should box the answers as per correct math.

So for Final Answer section, I'll list all.

Note: For #10, the correct answer is "diamond", even though the provided answer key says "circle" — likely an error in the key.

But since the task is to solve accurately, I'll proceed.