Investigate chance processes and develop, use, and evaluate ... - Free Printable

Let’s solve each question step by step.

First, look at the spinner. It is divided into 6 equal sections. The numbers on the sections are:

- Top right: 1
- Right middle: 1
- Bottom right: 2
- Bottom left: 3
- Left middle: 4
- Top left: 4

So the full list of outcomes (what you can land on) is:
1, 1, 2, 3, 4, 4

That means there are 6 total possible outcomes, and some numbers appear more than once.

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Question 1: What is the probability of the spinner landing on a 3?

How many sections have a “3”? → Only one section has a 3.

Total sections = 6

Probability = (number of favorable outcomes) / (total outcomes) = 1/6

✔ Answer for #1: 1/6

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Question 2: What is the probability of the spinner landing on a 1?

How many sections have a “1”? → Two sections (top right and right middle).

So, favorable outcomes = 2

Total outcomes = 6

Probability = 2/6 → which simplifies to 1/3

✔ Answer for #2: 1/3

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Question 3: What is the probability of the spinner landing on a 2?

How many sections have a “2”? → Only one section (bottom right).

Favorable outcomes = 1

Total outcomes = 6

Probability = 1/6

✔ Answer for #3: 1/6

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Question 4: Are you more likely to spin an odd number or an even number? Explain.

First, let’s list all the numbers again:
1, 1, 2, 3, 4, 4

Now separate them into odd and even:

Odd numbers: 1, 1, 3 → that’s three odd numbers
Even numbers: 2, 4, 4 → that’s three even numbers

Wait — both have 3 out of 6?

But let’s double-check:

- Odd: 1 (appears twice), 3 (once) → 2 + 1 = 3
- Even: 2 (once), 4 (twice) → 1 + 2 = 3

So actually, it’s equally likely to spin an odd or even number!

But wait — maybe I miscounted? Let me count the sections again from the image description:

Sections:
- 1 (odd)
- 1 (odd)
- 2 (even)
- 3 (odd)
- 4 (even)
- 4 (even)

Oh! Wait — that’s three odds and three evens? No:

Actually:

List with parity:

1 → odd
1 → odd
2 → even
3 → odd
4 → even
4 → even

So:

Odds: positions 1, 2, 4 → that’s three odds
Evens: positions 3, 5, 6 → that’s three evens

Yes — so 3 odd, 3 even → same chance.

But hold on — let me recount based on actual values:

Numbers: [1, 1, 2, 3, 4, 4]

Odd numbers: 1, 1, 3 → that’s 3 numbers
Even numbers: 2, 4, 4 → that’s 3 numbers

So probability of odd = 3/6 = 1/2
Probability of even = 3/6 = 1/2

They are equally likely.

But the question says: “Are you more likely to spin an odd number or an even number?”

If they’re equal, then neither is more likely.

But maybe I made a mistake? Let me check the spinner layout again as described:

From the image description:

Spinner sections (going clockwise from top?):

Top: 4
Right-top: 1
Right-bottom: 1
Bottom: 2
Left-bottom: 3
Left-top: 4

Wait — that would be:

Positions:

1. Top: 4 → even
2. Right-top: 1 → odd
3. Right-bottom: 1 → odd
4. Bottom: 2 → even
5. Left-bottom: 3 → odd
6. Left-top: 4 → even

So listing in order: 4, 1, 1, 2, 3, 4

Same as before: [4,1,1,2,3,4] → still 3 odd (1,1,3) and 3 even (4,2,4)

So yes — exactly half and half.

Therefore, you are not more likely to spin either — they are equally likely.

But the question asks: “Are you more likely to spin an odd number or an even number? Explain.”

Since they are equal, we should say: “Neither — you are equally likely to spin an odd or even number because there are 3 odd numbers and 3 even numbers on the spinner.”

✔ Final answer for #4: You are equally likely to spin an odd or even number because there are 3 odd numbers (1, 1, 3) and 3 even numbers (2, 4, 4) out of 6 total sections.

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Final Answers:

1. 1/6
2. 1/3
3. 1/6
4. You are equally likely to spin an odd or even number because there are 3 odd numbers and 3 even numbers on the spinner.

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Final Answer:
1. \(\frac{1}{6}\)
2. \(\frac{1}{3}\)
3. \(\frac{1}{6}\)
4. You are equally likely to spin an odd or even number because there are 3 odd numbers (1, 1, 3) and 3 even numbers (2, 4, 4) out of 6 total sections.