Experimental Probability Worksheet | Fun and Engaging PDF Worksheets - Free Printable

Since both ExplainAnswer and TeachTopic are false, we skip those sections entirely.

We also skip GeneratePractice, as it is also false.

That leaves only the Final Answer section — but since no specific question was asked to solve (the image contains multiple open-ended tasks for the student to complete themselves), and there’s no single numerical or factual answer requested, we must conclude:

→ There is no final answer to provide here because this is a worksheet meant for hands-on experimentation and reflection by the student. The problems require actual dice rolls, data recording, graphing, and personal interpretation — which cannot be done without performing the experiment.

However, if we interpret the request as “solve what can be solved from the given data”, then in Section B, some values are already filled in (Number of '6's at each trial count). We can calculate the experimental probabilities and theoretical probability based on that.

Let’s do that carefully.

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In Section B:

Theoretical probability of scoring a ‘6’ with a fair die = 1/6 ≈ 0.17 (to two decimal places)

But looking at the graph in Section B, the red dashed line is drawn at approximately 0.2 — suggesting maybe they’re using 1/5? Or perhaps it’s just an approximation. But mathematically, for a standard six-sided die, theoretical probability is always 1/6.

Wait — let’s check the data:

At 60 trials, number of ‘6’s = 50 → that’s extremely high! That suggests the die is NOT fair. In fact, 50 out of 60 is about 83% — way higher than 1/6 (~16.7%).

So perhaps in this context, “theoretical probability” refers to what you’d expect if the die were fair — i.e., still 1/6.

But let’s compute the experimental probabilities for Section B:

Formula:
Experimental Probability = (Number of ‘6’s) / (Number of Rolls)

For 10 rolls: 2/10 = 0.20
For 20 rolls: 16/20 = 0.80
For 30 rolls: 27/30 = 0.90
For 40 rolls: 30/40 = 0.75
For 50 rolls: 42/50 = 0.84
For 60 rolls: 50/60 ≈ 0.83

All rounded to two decimal places.

Theoretical probability (assuming fair die): 1/6 ≈ 0.17

Now, answering the questions in Section B:

1) What does the horizontal line (in red) represent?
→ It represents the theoretical probability of rolling a ‘6’ if the die were fair — which is 1/6 ≈ 0.17. But in the graph, it looks like it’s drawn at 0.2 — possibly rounded up for visibility. So we’ll say: It represents the expected probability if the die is fair.

2) Is the dice a fair dice? How can you tell from your graph?
→ No, it is not fair. The experimental probability (red jagged line) stays far above the theoretical line (around 0.2–0.9 instead of ~0.17). Even after many trials, it doesn’t converge toward 0.17 — meaning the die is biased.

3) How would the graph compare with the horizontal line (theory line) as the number of trials increase?
→ If the die were fair, the experimental probability line would get closer and closer to the theoretical line as trials increased. But since this die is clearly biased (getting too many 6s), even with more trials, it will likely stay far above the theoretical line — unless the bias changes.

But again — these are discussion answers, not calculable finals.

Given all this, and since the user didn’t ask a specific question to solve numerically, and per instructions we must give a Final Answer only if there’s one...

Actually — wait. Looking back at the original prompt: “Solve the problem accurately.”

There is no single “problem” stated — it’s a full worksheet.

Therefore, the most accurate response under the constraints is to note that no single final answer exists — but since we must output something in Final Answer, and considering Section B has computable parts...

Perhaps the intent is to fill in the table for Section B?

Let’s assume that’s what’s needed.

Completed Table for Section B:

| Number of Rolls | Number of '6's | Experimental probability of scoring '6' | Theoretical probability of scoring '6' |
|------------------|----------------|------------------------------------------|----------------------------------------|
| 10 | 2 | 0.20 | 0.17 |
| 20 | 16 | 0.80 | 0.17 |
| 30 | 27 | 0.90 | 0.17 |
| 40 | 30 | 0.75 | 0.17 |
| 50 | 42 | 0.84 | 0.17 |
| 60 | 50 | 0.83 | 0.17 |

These are calculated correctly.

And for the graph — it’s already plotted in the image, so no action needed.

Thus, if forced to give a “final answer”, it would be the completed table values.

But since the format requires only one final answer box, and we can't put a whole table...

Alternatively, perhaps the key insight is recognizing the die is unfair — but that’s qualitative.

Given ambiguity, and following strict rules: since no explicit question was posed to solve (like “what is X?”), and the task is experiential, I will state that no single final answer applies — but to comply with format, I’ll provide the theoretical probability value, which is constant.

Final Answer:
0.17