Probability with spinner activity - Free Printable

Let’s go through each question one by one, using the spinner info:

We’re told:
- blue = 5 sections
- yellow = 3 sections
- green = 3 sections
- red = 7 sections
- total = 18 sections

Probability is always:
favorable outcomes ÷ total outcomes

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1. Probability of landing on blue?
Blue has 5 sections → 5/18 ✔ (already done)

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2. Probability of NOT landing on blue?
Total sections = 18
Blue = 5 → Not blue = 18 - 5 = 13
→ 13/18 ✔

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3. Equal chance of yellow or green?
Yellow = 3, Green = 3 → same number → YES ✔

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4. Probability of landing on green OR yellow?
Green + Yellow = 3 + 3 = 6
→ 6/18 = simplify → divide top and bottom by 6 → 1/3 ✔

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5. Probability of NOT landing on red OR green?
Red + Green = 7 + 3 = 10
Not red or green = 18 - 10 = 8
Wait — let me double-check that.

Actually, “not landing on either red or green” means we want everything EXCEPT red and green.

So favorable = total - (red + green) = 18 - (7+3) = 18 - 10 = 8
→ 8/18 = simplify → divide by 2 → 4/9

But wait — the answer key says 4/6? That can’t be right. Let me check again.

Hold on — maybe I misread the question.

Question 5: “What is the probability of the spinner not landing either on either red or green?”

That wording is a bit awkward, but it likely means: “not landing on red AND not landing on green” → which is the same as “landing on blue or yellow”.

Blue = 5, Yellow = 3 → 5 + 3 = 8 → 8/18 = 4/9

But the answer key shows 4/6 — that must be a mistake in the key? Or did I misread?

Wait — let me look at the image again mentally.

In the image, for #5, the handwritten answer is 4/6 — but that doesn’t match our math.

Wait — perhaps they meant something else?

Alternative interpretation: Maybe “not landing on either red or green” was miswritten, and they meant “landing on red or green”? But no, the question says “not landing”.

Wait — let’s recalculate:

If “not landing on red or green”, then favorable = blue + yellow = 5 + 3 = 8 → 8/18 = 4/9

But 4/6 is 2/3 — which would be 12/18 — that’s too big.

Hmm — unless... maybe the question was supposed to say “landing on red or green”? Then 7+3=10 → 10/18 = 5/9 — still not 4/6.

Wait — 4/6 reduces to 2/3 — which is 12/18. What adds to 12? Blue + yellow + green = 5+3+3=11 — no. Red + blue = 7+5=12 → oh!

Maybe the question was misread? Let me read the original again:

“5. What is the probability of the spinner not landing either on either red or green?”

This is poorly worded. It probably means: “not landing on red and not landing on green” → i.e., landing on blue or yellow → 8/18 = 4/9

But the answer key says 4/6 — which is wrong.

Wait — perhaps it's a typo in the key? Or maybe I’m missing something.

Another thought: Maybe “either on either” is a double negative? No, that doesn’t make sense.

Perhaps the question meant: “What is the probability of landing on red or green?” — then 10/18 = 5/9 — still not 4/6.

Wait — 4/6 = 12/18 — what combination gives 12? Red + blue = 7+5=12 — yes!

So if the question was “landing on red or blue”, then 12/18 = 2/3 = 4/6 after simplifying? Wait, 12/18 simplifies to 2/3, and 4/6 also simplifies to 2/3 — so maybe they wrote 4/6 instead of 2/3? But why?

Actually, 12/18 = 2/3, and 4/6 = 2/3 — so numerically correct, but not simplified from 12/18.

But the instruction says: “Simplify if needed.” So 12/18 should become 2/3, not 4/6.

Unless they reduced 12/18 by dividing by 3? 12÷3=4, 18÷3=6 → 4/6 — but that’s not fully simplified. Usually we simplify to lowest terms.

But perhaps in this worksheet, they accept 4/6? Or maybe it’s a mistake.

Looking back at the image description — the user provided an image with answers filled in, including 4/6 for #5.

But according to strict math, 8/18 = 4/9 for “not red or green”.

I think there might be a misinterpretation of the question.

Let me parse the sentence: “not landing either on either red or green”

This is grammatically incorrect. Probably meant: “not landing on red or green” — meaning avoiding both.

Which is blue or yellow: 5+3=8 → 8/18=4/9

But the answer key says 4/6 — which suggests they calculated something else.

Wait — another possibility: maybe “not landing on either red or green” was intended to mean “landing on neither red nor green” — same thing.

Or perhaps it’s “not (landing on red or green)” — which is the same.

I think the answer key might have an error here. But since the user is showing the answer key, and we’re to solve accurately, I should go with correct math.

But let’s continue and see other questions.

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6. Equal chance of blue or red?
Blue = 5, Red = 7 → not equal → NO ✔

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7. Probability of NOT landing on yellow, blue, or green?
That means only red left.
Red = 7 → 7/18 ✔

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8. Probability of landing on red, blue, or green?
Red + Blue + Green = 7 + 5 + 3 = 15
→ 15/18 = simplify → divide by 3 → 5/6 ✔

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9. Probability of NOT landing on red or yellow?
Not red and not yellow → so blue or green
Blue + Green = 5 + 3 = 8
→ 8/18 = 4/9 ✔

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10. Equal chance of red or green?
Red = 7, Green = 3 → not equal → NO ✔

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Now back to #5: The correct answer should be 4/9, but the key says 4/6. Since 4/6 is equivalent to 2/3, and 2/3 of 18 is 12, which would be red + blue = 7+5=12, perhaps the question was misstated, and it should be “landing on red or blue”?

But the question as written is “not landing either on either red or green” — which is confusing.

Given the context, and that all other answers match except possibly #5, and since the user is presenting the answer key, I suspect there might be a typo in the question or key.

However, for accuracy, I will calculate based on standard interpretation.

“Not landing on red or green” = landing on blue or yellow = 5+3=8 → 8/18 = 4/9

But let’s check the total: blue 5, yellow 3, green 3, red 7 — sum 18, good.

For #5, if we take “not landing on red or green”, it’s 8/18=4/9.

But the answer key has 4/6 — which is incorrect for that question.

Perhaps the question was: “What is the probability of landing on red or blue?” — then 7+5=12 → 12/18=2/3=4/6 if not fully simplified.

And the instruction says “simplify if needed” — 12/18 can be simplified to 2/3, but 4/6 is also correct numerically, though not simplest form.

In many classrooms, they might accept 4/6 if students reduce by 3, even though 2/3 is better.

But strictly speaking, 4/9 is correct for the question as written.

However, looking at the pattern, and since the user included the answer key with 4/6, and to avoid confusion, I’ll note that there might be a discrepancy, but for the sake of matching the expected answer, perhaps they meant "landing on red or blue".

But I think it's safer to go with correct math.

Let me see question 9: "not landing on either red or yellow" — which we did as blue or green = 8/18=4/9 — and key has 4/9, good.

For consistency, #5 should be similar.

Perhaps the question #5 is "not landing on red or green", which is blue or yellow = 8/18=4/9.

I think the answer key has a mistake for #5.

But since the user is asking to solve accurately, I'll provide the correct answer.

Final decision: For #5, correct answer is 4/9.

But let's list all answers as per calculation:

1. 5/18
2. 13/18
3. Yes
4. 1/3
5. 4/9 [corrected from key's 4/6]
6. No
7. 7/18
8. 5/6
9. 4/9
10. No

However, upon second thought, let's re-read question 5: "What is the probability of the spinner not landing either on either red or green?"

The phrase "either on either" is redundant and likely a typo. Probably meant "not landing on red or green".

In probability, "not A or B" usually means not (A or B), which is neither A nor B.

So favorable outcomes are those that are not red and not green, i.e., blue or yellow: 5+3=8, so 8/18=4/9.

I think the answer key is wrong for #5.

But to respect the user's input, and since they might expect the key's answer, I'm conflicted.

No — the instruction is to solve accurately. So I'll go with 4/9.

Perhaps in the image, the handwriting is 4/9, but described as 4/6? Unlikely.

Another idea: maybe "not landing either on either" means something else, but I think it's safe to assume it's "not landing on red or green".

So I'll proceed with 4/9 for #5.

Now, compiling all answers:

1. 5/18
2. 13/18
3. Yes
4. 1/3
5. 4/9
6. No
7. 7/18
8. 5/6
9. 4/9
10. No

But let's verify #5 once more.

Total sections: 18
Red: 7, Green: 3 → together 10
Not red or green: 18-10=8 → 8/18=4/9 — yes.

Whereas 4/6 would be for 12 sections, which is red+blue=12, so if the question was "landing on red or blue", then 12/18=2/3=4/6.

Given that, and since the question says "not landing", I think it's a error in the key.

For the purpose of this response, I'll provide the mathematically correct answers.

Final Answer:
1. \frac{5}{18}
2. \frac{13}{18}
3. Yes
4. \frac{1}{3}
5. \frac{4}{9}
6. No
7. \frac{7}{18}
8. \frac{5}{6}
9. \frac{4}{9}
10. No