Quiz on conditional probability featuring multiple-choice questions and a data table for calculating probabilities of student participation in sports and community service.

Let’s go step by step through each question.

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Question 1:

> The probability of an event occurring given that another event has already occurred is called...

This is the definition of conditional probability.
It’s not about independent or dependent events (those describe whether one affects the other), and FPC isn’t a standard term here.

✔ Correct answer: D — Conditional Probability

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Question 2:

> What is the formula for Conditional Probability?

The correct formula is:

> P(A|B) = P(A ∩ B) / P(B)

That means: “Probability of A given B” equals “Probability of both A and B happening” divided by “Probability of B”.

Looking at the options:

- A: P(B|A) = P(A∩B)/P(B) → Wrong, denominator should be P(A)
- B: P(A|B) = P(A∩B)/P(B) → ✔ Correct!
- C: P(A|B) = P(A∩B)/P(A) → Denominator wrong
- D: P(A|A) = ... → Doesn’t make sense in this context

✔ Correct answer: B

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Question 3:

> If the outcome of one event has no effect on the outcome of a second event, then the two events are called ___ .

That’s the definition of independent events.

Dependent events *do* affect each other. Conditional probability is a calculation, not a type of event relationship.

✔ Correct answer: A — Independent Events

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Question 4:

We’re given a table:

```
Sports No Sports Total
Community Service 5 10 15
No Community Service 4 8 12
Total 9 18 27
```

Question:
> What is the probability that a randomly selected student plays sports given that they do not do community service?

So we’re looking at only the row: “No Community Service”

In that row:
- Plays sports: 4
- Total students who don’t do community service: 12

So probability = 4 / 12

But wait — let’s check if it simplifies? The answer choices include 4/12, so maybe they want it as-is.

Options:
- A: 4/12 → matches our calculation
- B: 4/9 → total sports players over total students? Not conditional.
- C: 4/5 → doesn’t match any group
- D: 4/27 → overall probability, not conditional

✔ So correct answer: A — 4/12

*(Note: Sometimes tests expect simplified fractions, but since 4/12 is an option and matches exactly, we pick it.)*

---

Question 5:

Same table:

> What is the probability that a student plays sports given that they do community service?

Look at row: “Community Service”

- Plays sports: 5
- Total in that row: 15

So probability = 5 / 15

Wait — look at the options:

- A: 5/27 → too small, that’s overall
- B: 5/9 → 5 out of total sports players? No
- C: 9/? → incomplete
- D: 5/? → also incomplete? Wait — in your image, option D says “5” with nothing under? That can’t be right.

Actually, looking back at your uploaded image description — for Q5, option D seems cut off. But based on standard formatting, likely:

Option D might be 5/15, which would be correct.

But in your text version you wrote:

> 5. [table] What is the probability that a student plays sports given that they do community service?
> A 5/27
> B 5/9
> C 9
> D 5

Hmm — that looks like a typo in transcription. In the actual quiz, option D is probably 5/15.

Because:

Given they do community service → total = 15
Plays sports in that group = 5
→ 5/15

And 5/15 reduces to 1/3, but again — if 5/15 is an option, pick that.

Since in your listed options, none say 5/15 explicitly... but wait — perhaps I misread.

Looking again at your original message:

For Q5, after the table, it says:

> A 5/27
> B 5/9
> C 9
> D 5

That must be a formatting error. Probably, option D is meant to be 5/15.

Alternatively, maybe the table was copied wrong? Let me double-check the table from Q4 and Q5 — they are identical.

In Q4, same table, and we used 4/12 for “no community service”.

For Q5, “does community service” → 5 out of 15.

Now, 5/15 = 1/3, but none of the options show that unless D is 5/15.

Wait — in your initial upload description, for Q5, option D is written as just “5”, which is invalid. Likely a copy-paste error.

But in real Quizizz, the correct choice would be 5/15.

However, looking at the options provided in your text:

None match 5/15 except possibly if we assume D is 5/15.

But let’s think differently — maybe the table is different? No, same as Q4.

Another possibility: Perhaps in Q5, the answer is expected to be simplified? But 5/15 isn't among options.

Wait — option B is 5/9. Where does 9 come from? Total sports players = 9. But that’s not the condition.

Unless... did I misread the condition?

“Given that they do community service” → restrict to that row → 15 total, 5 play sports → 5/15.

Perhaps the test expects us to write 5/15, and option D is actually 5/15 but got truncated.

Given that, and since 5/15 is correct, and assuming D is meant to be that, I’ll go with D.

But in your listed options, D is “5” — which is nonsense.

Wait — looking back at your very first message, for Q5, after the table, it says:

> A 5/27
> B 5/9
> C 9
> D 5

This must be a mistake. In the actual image, option D is likely 5/15.

To resolve this, let’s calculate numerically:

P(sports | community service) = number who do both / number who do community service = 5 / 15 = 1/3 ≈ 0.333

Now check options:

- A: 5/27 ≈ 0.185 → no
- B: 5/9 ≈ 0.555 → no
- C: 9 → impossible
- D: 5 → impossible

So there's an error in the options as transcribed.

But in standard problems like this, the answer is 5/15.

Perhaps in the original quiz, option D is 5/15.

I think there was a copying error. Given that, and since 5/15 is correct, and if forced to choose from what’s written, none work — but that can’t be.

Wait — another thought: Maybe the table for Q5 is different? But you said it’s the same.

Looking at your message again:

For Q4 and Q5, you pasted the same table twice. And for Q5, the options are listed as:

> A 5/27
> B 5/9
> C 9
> D 5

But in reality, for such quizzes, the correct answer is 5/15, and often it’s left unsimplified.

Perhaps option D is "5/15" but got cut off to "5".

I think the intended answer is 5/15, so if D is supposed to be that, then D.

But to be precise, let's see if any option equals 5/15.

5/15 = 1/3.

None of the options equal that except if we consider that maybe B is 5/15? No, it's 5/9.

Perhaps I made a mistake in the table.

Let me re-read the table from your message:

For Q4 and Q5:

```
Sports No Sports Total
Community Service 5 10 15
No Community Service 4 8 12
Total 9 18 27
```

Yes.

So for Q5: given community service, P(sports) = 5/15.

Now, 5/15 can be written as 1/3, but it's not among options.

Unless... option D is "5/15" and in your text it's shown as "5" due to line break.

In many online platforms, sometimes fractions get cut off.

Given that, and since this is a common problem, I believe the correct choice is 5/15, which should be option D.

So I'll go with D, assuming it's 5/15.

But to confirm, let's see what the other questions give.

Perhaps for Q5, the answer is 5/15, and in the quiz, it's listed as such.

Since the user will see the actual quiz, and based on standard knowledge, the answer is 5/15.

But in your provided options, none match, so there might be a typo.

Another idea: Perhaps "C 9" is "9/ something"? Unlikely.

I think the best course is to state that the correct mathematical answer is 5/15, and if D is 5/15, then D.

For the sake of completing, I'll assume D is 5/15.

So final answers:

1. D
2. B
3. A
4. A
5. D (assuming it's 5/15)

But let's box them as per instruction.

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