Math worksheet on spinner probability with critical thinking questions.

Let's solve each question step by step based on the spinner shown in the image. The spinner is divided into 8 equal sections, with the following amounts:

- $500
- $150
- $85
- $100
- $25
- $0
- $50
- $75

Since the spinner has 8 equal sections, each outcome has a probability of 1/8.

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1. What is the probability of landing on $500?

There is one section with $500 out of 8 total sections.

✔ Answer:
$$
\frac{1}{8}
$$

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2. What is the probability of landing on an amount over $100?

First, identify the values over $100:
- $150
- $500
- $85 → no (less than $100)
- $100 → not *over*, so exclude
- $75, $50, $25, $0 → all less than $100

So only $150 and $500 are over $100.

That’s 2 sections.

✔ Answer:
$$
\frac{2}{8} = \frac{1}{4}
$$

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3. What is the probability of landing on $100 in two successive spins?

The probability of landing on $100 in one spin is 1/8.

Since spins are independent:
$$
P(\text{$100 then $100}) = \frac{1}{8} \times \frac{1}{8} = \frac{1}{64}
$$

✔ Answer:
$$
\frac{1}{64}
$$

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4. John earns $200 in 3 spins. Name all the possible ways he could have achieved this feat.

We need to find all combinations of three numbers from the spinner that add up to $200.

Available values: $0, $25, $50, $75, $85, $100, $150, $500

We want combinations of three spins (order doesn't matter for listing possibilities, but since spins are ordered, we can list unordered triples or consider permutations — but here, just list distinct combinations).

Let’s look for combinations of three values (repetition allowed) that sum to $200.

Try different combinations:

#### Try: $100 + $100 + $0 = $200 ✔
→ Possible: ($100, $100, $0)

#### Try: $100 + $75 + $25 = $200 ✔
→ ($100, $75, $25)

#### Try: $100 + $50 + $50 = $200 ✔
→ ($100, $50, $50)

#### Try: $75 + $75 + $50 = $200 ✔
→ ($75, $75, $50)

#### Try: $85 + $85 + $30 → no $30 → invalid

#### Try: $85 + $75 + $40 → no $40 → invalid

#### Try: $85 + $50 + $65 → no $65 → invalid

#### Try: $150 + $50 + $0 = $200 ✔
→ ($150, $50, $0)

#### Try: $150 + $25 + $25 = $200 ✔
→ ($150, $25, $25)

#### Try: $100 + $85 + $15 → no $15 → invalid

#### Try: $50 + $50 + $100 → already counted

Now check if any others:

#### Try: $75 + $50 + $75 → same as above

#### Try: $85 + $100 + $15 → no

#### Try: $25 + $25 + $150 → already listed

#### Try: $0 + $100 + $100 → already listed

#### Try: $50 + $50 + $100 → already listed

#### Try: $25 + $75 + $100 → already listed

Is there a way with $85?

Try: $85 + $85 + $30 → no

$85 + $75 + $40 → no

$85 + $50 + $65 → no

$85 + $25 + $90 → no

So only valid combinations:

1. $100, $100, $0
2. $100, $75, $25
3. $100, $50, $50
4. $75, $75, $50
5. $150, $50, $0
6. $150, $25, $25

✔ Answer:
- $100, $100, $0
- $100, $75, $25
- $100, $50, $50
- $75, $75, $50
- $150, $50, $0
- $150, $25, $25

(Note: Order doesn’t matter here unless asked for permutations.)

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5. You earn 3 spins. On your first two spins you earn $250. What is the probability that the total of your 3 spins will be greater than $300?

You’ve already earned $250 in first two spins.

So you need the third spin to be such that:
$$
\text{Total} > 300 \Rightarrow \text{Third spin} > 300 - 250 = 50
$$

So third spin must be greater than $50.

What values on the spinner are > $50?

- $75 ✔
- $85 ✔
- $100 ✔
- $150 ✔
- $500 ✔

Note: $50 is not greater than $50, so excluded.

So values > $50: $75, $85, $100, $150, $500 → that’s 5 values

Each has probability $ \frac{1}{8} $

So probability:
$$
\frac{5}{8}
$$

✔ Answer:
$$
\frac{5}{8}
$$

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6. You earn 3 spins.

#### A) What is the lowest amount of money you could earn?

Minimum value per spin is $0.

So minimum total = $0 + $0 + $0 = $0

✔ Answer: $0

#### B) What is the probability of spinning that amount?

To get $0 total, all three spins must be $0.

Probability of $0 on one spin = $ \frac{1}{8} $

So:
$$
P(\text{all } \$0) = \frac{1}{8} \times \frac{1}{8} \times \frac{1}{8} = \frac{1}{512}
$$

✔ Answer: $ \frac{1}{512} $

#### C) What is the greatest amount of money you could earn?

Maximum value per spin = $500

So maximum total = $500 × 3 = $1500

✔ Answer: $1500

#### D) What is the probability of spinning that amount?

Only possible if all three spins land on $500.

Probability = $ \frac{1}{8} \times \frac{1}{8} \times \frac{1}{8} = \frac{1}{512} $

✔ Answer: $ \frac{1}{512} $

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✔ Final Answers Summary:

1. $ \frac{1}{8} $
2. $ \frac{1}{4} $
3. $ \frac{1}{64} $
4. Possible combinations:
- $100, $100, $0
- $100, $75, $25
- $100, $50, $50
- $75, $75, $50
- $150, $50, $0
- $150, $25, $25
5. $ \frac{5}{8} $
6.
A) $0
B) $ \frac{1}{512} $
C) $1500
D) $ \frac{1}{512} $

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