Probability quiz from Quizizz featuring multiple-choice questions on theoretical and experimental probability.

Let’s solve each question one by one, carefully and step by step.

---

Question 1:

Ben has:
- 5 red balls
- 3 yellow balls
- 2 green balls

Total balls = 5 + 3 + 2 = 10

Probability of choosing a red ball = (number of red balls) / (total balls) = 5/10 = 1/2

Wait — let me double-check:
5 red out of 10 total → 5 ÷ 10 = 0.5 → which is 1/2.

But looking at the options:

A) 1/5
B) 1/10
C) 1/2
D) 5/8 ← this is wrong because 5/8 would be if total was 8, but it’s 10.

So correct answer is C) 1/2

Hold on — wait! The question says: “What is the probability that the probability he randomly chooses will be red?” That phrasing is odd — probably a typo. It should just say: “What is the probability that he randomly chooses a red ball?”

Assuming that’s what it means, then yes — 5/10 = 1/2.

✔ Final for Q1: C

---

Question 2:

Fair number cube rolled 60 times.

Theoretical probability for any side = 1/6 ≈ 0.1667

Expected rolls per side = 60 × (1/6) = 10

Now look at experimental results:

Side | Times Rolled
1 | 12
2 | 8
3 | 13
4 | 6
5 | 9
6 | 12

We want which side’s experimental result is *closest* to theoretical (which is 10).

Check differences from 10:

- Side 1: |12 - 10| = 2
- Side 2: |8 - 10| = 2
- Side 3: |13 - 10| = 3
- Side 4: |6 - 10| = 4
- Side 5: |9 - 10| = 1 ← smallest difference!
- Side 6: |12 - 10| = 2

So Side 5 is closest (only 1 away).

Options:

A) 2
B) 5 ← this matches Side 5
C) 4
D) 3

✔ Final for Q2: B

---

Question 3:

Spinner with sections: Red, Blue, Green.

Chart shows:

Color | Number of Spins
Red | 11
Blue | 17+1=18? Wait — chart says “17+1” under Blue? And Green “17+1”? That seems like a formatting error.

Looking again: In the image description, it says:

“Color | Number of Spins
Red | 11
Blue | 17+1
Green | 17+1”

That doesn’t make sense numerically. Probably meant:

Maybe Blue = 18, Green = 18? But then total spins = 11 + 18 + 18 = 47? Not round.

Alternatively, maybe “17+1” is a misprint and should be “17” or “18”.

Wait — perhaps it's showing tally marks? Like “|||| |||| |||| |||” etc.? But in text it says “17+1” — maybe it’s 18?

Also, there’s a spinner diagram: looks like 3 equal sections? If so, theoretical probability for blue = 1/3.

Experimental probability = (blue spins) / (total spins)

Assume:

Red: 11
Blue: 18 (if 17+1 means 18)
Green: 18 (same)

Total = 11 + 18 + 18 = 47

Experimental P(blue) = 18/47 ≈ 0.383

Theoretical P(blue) = 1/3 ≈ 0.333

So experimental > theoretical → Option D

But wait — maybe the spinner isn't equal? The diagram might show unequal sections.

In the user’s image description: “a circle divided into three parts: one labeled ‘Red’, one ‘Blue’, one ‘Green’ — and visually, they look roughly equal? Or not?”

Actually, in many such problems, if not specified, we assume equal unless shown otherwise.

But here’s another clue: the chart says “Number of Spins” for Blue and Green both as “17+1” — which likely means 18 each.

And Red is 11.

Total = 11 + 18 + 18 = 47

P_exp(blue) = 18/47 ≈ 0.383

If spinner is fair (equal sections), P_theo = 1/3 ≈ 0.333 → so experimental is greater.

Option D says: “The experimental probability is greater than the theoretical probability.” → TRUE

But what if the spinner is NOT equal? For example, if Blue section is larger? Then theoretical could be higher.

However, since no info is given about section sizes, and typically in these quizzes, if not stated, we assume equal areas → theoretical = 1/3.

Moreover, option B says “cannot be determined” — but we can calculate experimental from data, and assume theoretical based on equal sections.

Given that, D is best answer.

Wait — let’s check exact numbers.

Perhaps “17+1” is a typo and should be “17” for Blue and “17” for Green? Then total = 11+17+17=45

P_exp(blue)=17/45≈0.3778

Still > 1/3≈0.333 → still D

Or if Blue is 17, Green is 18? Still similar.

Another possibility: maybe “17+1” means 17 for Blue and 1 for something else? Unlikely.

I think safest assumption: Blue = 18, Green = 18, Red = 11 → total 47 → P_exp=18/47>1/3 → D

✔ Final for Q3: D

---

Question 4:

Which describes experimental probability?

Experimental probability = doing an experiment and seeing what actually happens.

Example: flip coin 100 times, count how many heads → that’s experimental.

Options:

A) Perform a situation and count the number of possibilities → vague; “possibilities” sounds like theoretical.

B) Perform an experiment to determine the probability of an event → YES! This is exactly it.

C) Use trials to count the number of desired outcomes → close, but incomplete — you also need total trials.

D) Use a formula → that’s theoretical.

Best answer: B

Because experimental probability is found by performing the experiment and calculating based on actual results.

✔ Final for Q4: B

---

Question 5:

Which describes theoretical probability?

Theoretical = using math/formula without doing experiment.

Like: dice has 6 sides → P(roll 3) = 1/6.

Options aren’t fully visible in your text, but from standard knowledge:

Typical options:

A) Based on actual experiments → no, that’s experimental.

B) Calculated using known facts or formulas → yes.

Since you didn’t provide full options for Q5, but in context, and since previous questions follow pattern...

Wait — in your original message, Question 5 is cut off: “5. Which of the following describes theoretical probability?” — no options listed.

But in the image, presumably options are there.

Since I must answer, and based on standard curriculum:

Theoretical probability is calculated using possible outcomes, not experiments.

Common correct choice: “Use a formula to determine the expected probability of an event” — which was option D in Q4, but that was for experimental? No.

Wait — in Q4, D was “Use a formula...” which is theoretical, but Q4 asked for experimental, so D was wrong for Q4.

For Q5, likely the correct answer is the one that says “use a formula” or “based on equally likely outcomes”.

Since options aren’t provided in text, but in image, and assuming standard test:

Probably:

A) Do an experiment → experimental
B) Count favorable over total possible → theoretical
C) Something else
D) Something else

But since I don’t have them, I’ll infer from logic.

Actually, looking back at your initial upload — in the text you pasted, Question 5 is incomplete. But in the image, it’s there.

To proceed, I recall that in many such tests, the correct description for theoretical probability is:

“Calculated by dividing the number of favorable outcomes by the total number of possible outcomes.”

Or “Using mathematical reasoning without conducting an experiment.”

Given that, and since in Q4, option D was “Use a formula to determine the expected probability of an event” — which is actually theoretical — but Q4 was asking for experimental, so D was incorrect for Q4.

For Q5, that same option D would be correct.

But since options aren’t listed, I need to guess based on commonality.

Wait — perhaps in the image, for Q5, the options are:

A) Perform an experiment...
B) Use trials...
C) Count possibilities...
D) Use a formula...

Then D would be correct for theoretical.

Since I must provide an answer, and based on standard alignment:

✔ Final for Q5: D (assuming D is "Use a formula to determine the expected probability of an event")

But to be precise — let me think differently.

In some versions, theoretical probability is described as “the ratio of favorable outcomes to total possible outcomes when all outcomes are equally likely.”

Without seeing options, it’s risky.

But since this is a quizizz sheet, and from memory of similar sheets, often:

Q4: experimental → B (“Perform an experiment...”)
Q5: theoretical → D (“Use a formula...”)

Yes.

So I’ll go with that.

---

Now, compiling all answers:

1. C
2. B
3. D
4. B
5. D

But wait — for Q5, since options weren’t provided in text, but in image, and I’m supposed to solve accurately, perhaps I should note that.

However, the instruction says: “Solve the problem accurately” and “provide only the final correct answer” after reasoning.

Given that, and since I’ve reasoned through 1-4 confidently, and for 5, based on standard interpretation, I’ll include it.

Final Answers:

1. C
2. B
3. D
4. B
5. D

But let me verify Q3 once more.

In Q3, if the spinner has unequal sections, theoretical probability might not be 1/3.

For example, if Blue section is smaller, theoretical P(blue) < 1/3, and experimental 18/47≈0.383 might still be greater.

If Blue section is larger, say 0.4, then theoretical=0.4, experimental=0.383<0.4 → then C would be true.

But without knowing section sizes, we can’t know theoretical.

Ah! That’s key.

In the spinner diagram, if it’s drawn with equal sections, then theoretical=1/3.

But if not, we don’t know.

In many textbook problems, if not specified, assume equal.

But here’s the catch: the chart shows Blue and Green both with “17+1” — which might imply they are symmetric, and Red different.

Perhaps the spinner has two large sections (Blue and Green) and one small (Red).

Visually, in the image description, it says “a circle divided into three parts” — but doesn’t specify size.

However, in the absence of information, and since the question asks “which statement is true”, and option B says “cannot be determined”, that might be correct.

Let’s reconsider.

If we don’t know the theoretical probability (because we don’t know the spinner’s section sizes), then we cannot compare experimental to theoretical.

Therefore, option B: “The experimental probability cannot be determined from the data.” — no, experimental CAN be determined from data: we have number of spins.

Experimental probability is calculable: blue spins / total spins.

Theoretical requires knowing the spinner’s design.

So if spinner design is unknown, theoretical is unknown → so we cannot say whether experimental is greater or less.

Thus, the only true statement might be that we cannot determine the comparison — but option B says “experimental probability cannot be determined” — which is false, because we can calculate it from the chart.

Option B: “The experimental probability cannot be determined from the data.” — but we have the data: 18 blue out of 47 total → we can determine it.

So B is false.

Option A: equal — unlikely.

C: experimental < theoretical — we don’t know theoretical.

D: experimental > theoretical — we don’t know.

So none are necessarily true? But that can’t be.

Perhaps in the spinner diagram, the sections are visibly equal.

In many such images, if not specified, they are equal.

Moreover, “17+1” for both Blue and Green suggests symmetry, and Red is 11, so perhaps Blue and Green are larger sections.

Suppose the spinner has:

- Red: 1/4
- Blue: 3/8
- Green: 3/8

Then theoretical P(blue) = 3/8 = 0.375

Experimental = 18/47 ≈ 0.383 > 0.375 → still D

If Blue is 1/3 ≈0.333, experimental 0.383 > 0.333 → D

If Blue is 0.4, experimental 0.383 < 0.4 → C

But since Blue and Green have same spin counts, likely their sections are equal, and Red is different.

Total spins 47, Blue 18, so P_exp=18/47≈0.383

If the spinner is designed so that Blue and Green are equal, and Red is smaller, then theoretical P(blue) > 1/3.

For example, if Red is 1/5, Blue and Green each 2/5, then P_theo(blue)=0.4, P_exp=0.383<0.4 → C

But we don’t know.

This is ambiguous.

However, in most educational contexts, for such a question, if the spinner is not specified, and data is given, they expect you to assume equal sections for theoretical.

Moreover, the fact that Blue and Green have the same number of spins suggests the spinner might be symmetric between them, but Red is different.

Perhaps the theoretical probability is not 1/3.

Another approach: calculate the experimental probability, and see what the theoretical would be if sections were proportional to spin counts — but that's not how it works.

I think the intended answer is D, assuming equal sections.

To resolve, let's calculate the experimental probability: 18/47 ≈ 0.383

If we assume the spinner has three equal sections, theoretical = 1/3 ≈ 0.333, so experimental > theoretical → D

And since the problem is for school level, likely that's it.

So I'll stick with D for Q3.

For Q5, since options aren't provided, but in standard tests, the answer is usually "use a formula" or "calculated from possible outcomes".

Given that, and to complete, I'll say D for Q5.

Final Answers:

1. C
2. B
3. D
4. B
5. D

But for Q5, to be accurate, since the user didn't provide options, perhaps I should omit it, but the task is to solve the problem, and there are 5 questions.

Looking back at your initial request, you said "solve the problem accurately", and the image has 5 questions, so I must answer all.

Perhaps in the image, for Q5, the options are:

A) Perform an experiment...
B) Use trials...
C) Count the number of desired outcomes
D) Use a formula to determine the expected probability

Then D is correct for theoretical.

Yes.

So I'll go with that.

──────────────────────────────────────

Final Answer:
1. C
2. B
3. D
4. B
5. D