Completed answer key showing solutions for experimental probability problems involving dice rolls and a color spinner.

Let’s solve this step by step.

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Problem 1: Rolling a die 20 times

You rolled the die 20 times and got these numbers:
6, 5, 5, 4, 6, 3, 2, 2, 1, 4, 5, 3, 2, 5, 4, 4, 1, 2, 3, 3

First, let’s count how many times each number came up:

- 1: appears at positions 9 and 17 → 2 times
- 2: appears at positions 7, 8, 13, 18 → 4 times
- 3: appears at positions 6, 12, 19, 20 → 4 times
- 4: appears at positions 4, 10, 15, 16 → 4 times
- 5: appears at positions 2, 3, 11, 14 → 4 times
- 6: appears at positions 1, 5 → 2 times

Total = 2 + 4 + 4 + 4 + 4 + 2 = 20 ✔ (matches total rolls)

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Part a: Experimental Probability of rolling each number?

Experimental probability = (number of times it happened) ÷ (total number of trials)

So:

- P(1) = 2/20 = 1/10 or 0.1
- P(2) = 4/20 = 1/5 or 0.2
- P(3) = 4/20 = 1/5 or 0.2
- P(4) = 4/20 = 1/5 or 0.2
- P(5) = 4/20 = 1/5 or 0.2
- P(6) = 2/20 = 1/10 or 0.1

*(Note: The answer key says “a. What is the Experimental Probability...” but doesn’t list answers — so we calculate based on data.)*

Wait — looking back at the image, under part b, it says:

> Based on the results of the experiment, if you rolled the dice 100 times, how many times would you expect to roll a 4? 100 × 4/20 = 20 times.

That matches our count: 4 appeared 4 times out of 20 → 4/20 = 1/5 → 100 × 1/5 = 20 ✔️

Similarly for others:

c. Roll a 2 or 5?
→ 2 appeared 4 times, 5 appeared 4 times → total 8 times in 20 rolls
→ 8/20 = 2/5
→ For 300 rolls: 300 × 8/20 = 300 × 0.4 = 120 times ✔️ (matches key)

d. Roll an odd number (1, 3, 5)?
→ 1: 2 times, 3: 4 times, 5: 4 times → total 10 times in 20 rolls
→ 10/20 = 1/2
→ For 200 rolls: 200 × 1/2 = 100 times ✔️ (matches key)

So all calculations check out.

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Problem 2: Spinning a spinner

Spinner has 4 colors: Yellow, Green, Blue, Red
Each section looks equal? But from the bar graph:

Yellow: 24
Green: 48
Blue: 16
Red: 32

Total spins = 24 + 48 + 16 + 32 = 120

Check: 24+48=72; 16+32=48; 72+48=120 ✔️

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Part a: Experimental Probability of spinning each color?

P(Yellow) = 24/120 = 1/5 or 0.2
P(Green) = 48/120 = 2/5 or 0.4
P(Blue) = 16/120 = 2/15 ≈ 0.133...
P(Red) = 32/120 = 4/15 ≈ 0.266...

But the answer key writes them as fractions over 120? Or simplified?

Looking at key:

It says:

Yellow: 24 / 120
Green: 48 / 120
Blue: 16 / 120
Red: 32 / 120

They didn’t simplify — probably because next parts use those numbers directly.

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Part b: If spun 150 times, how many times expect blue?

Blue occurred 16 times in 120 spins → probability = 16/120

Expected in 150 spins: 150 × (16/120)

Simplify: 150 ÷ 120 = 5/4 → 5/4 × 16 = 5 × 4 = 20 times ✔️ (matches key)

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Part c: If spun 200 times, how many times expect red?

Red: 32/120

200 × (32/120) = ?

Simplify: 200 ÷ 120 = 5/3 → 5/3 × 32 = 160/3 ≈ 53.333...

But key says: 200 × 32/120 = 53⅓ times → which is correct.

We can write as mixed number: 53 and 1/3 times

Since you can’t spin a third of a time, in real life you’d say about 53 times, but mathematically it’s 53⅓.

Key shows: 53⅓ times ✔️

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All answers match the key when calculated correctly.

Final Answer:

For Problem 1:
a. Experimental probabilities:
P(1)=2/20, P(2)=4/20, P(3)=4/20, P(4)=4/20, P(5)=4/20, P(6)=2/20
b. 20 times
c. 120 times
d. 100 times

For Problem 2:
a. P(Yellow)=24/120, P(Green)=48/120, P(Blue)=16/120, P(Red)=32/120
b. 20 times
c. 53⅓ times