Math worksheet focusing on compound probability problems involving spinners and bags of marbles.

Let’s solve each problem one by one, step by step.

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Problem 1:

Ricardo has a spinner with 4 equal sections: red, yellow, blue, green.
So, probability of spinning red = 1 out of 4 → 1/4

He also has a bag with:
- 2 red marbles
- 3 green marbles
- 3 blue marbles
Total marbles = 2 + 3 + 3 = 8

Probability of picking a red marble = 2 out of 8 → 2/8 = 1/4

We want the probability that BOTH happen: spin red AND pick red marble.
Since these are independent events, we multiply:

→ (1/4) × (1/4) = 1/16

✔ Final Answer for Problem 1: D) 1/16

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Problem 2:

Tossing a coin → 2 outcomes: heads or tails
Rolling a die → 6 outcomes: 1, 2, 3, 4, 5, 6

Total combined outcomes = 2 × 6 = 12

✔ Final Answer for Problem 2: D) 12

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Problem 3:

Bag has:
- Red marbles: let’s count from image — there are 3 red
- Blue marbles: 4 blue (from image: 4 blue dots)
Wait — actually, looking at the drawing in question 3:
There are 3 red and 4 blue? Let me recount carefully.

Actually, in the image for Q3:
Red marbles: 3
Blue marbles: 4
Total = 7 marbles

Question: Pick a blue marble, put it back, then pick a red marble.

Since you put it back, the total stays 7 both times.

P(blue first) = 4/7
P(red second) = 3/7

Multiply: (4/7) × (3/7)

That matches option C.

✔ Final Answer for Problem 3: C) 4/7 × 3/7

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Problem 4:

Spinner has 6 equal sections:
From image:
- Red: 2 sections
- Blue: 2 sections
- Green: 1 section
- Yellow: 1 section

Wait — let’s list them as shown:

Looking at the spinner in Q4:
It’s divided into 6 parts:
Top: Red
Right-top: Yellow
Right-bottom: Blue
Bottom: Red
Left-bottom: Green
Left-top: Blue

So:
Red: 2
Blue: 2
Green: 1
Yellow: 1
Total = 6

Probability of landing on green in one spin = 1/6

Spin two times, want green both times → independent events

(1/6) × (1/6) = 1/36

But wait — none of the options are given here? The user didn’t provide multiple choice for Q4? Actually, looking back — the original image shows only up to Q4 text, but no answer choices listed for Q4. Hmm.

Wait — rechecking the user input: In the image description, for Q4, it says:

> If you spin two times, what is the probability of landing on green both times?

And the spinner has 6 sections: 1 green.

So P(green) = 1/6 per spin.

Two spins: (1/6) × (1/6) = 1/36

But since no options are provided in the text for Q4, perhaps the user expects us to compute it anyway.

However, in the initial upload, maybe the options were cut off? But based on what’s written, we’ll go with calculation.

But wait — let me double-check the spinner in Q4.

In the image described:
The spinner for Q4 has:

- Top: Red
- Right: Yellow
- Bottom-right: Blue
- Bottom: Red
- Bottom-left: Green
- Top-left: Blue

Yes — so green is only 1 out of 6.

So answer is 1/36.

But since no options are given in the text for Q4, and the user might have intended to include them, but they’re missing — however, in the context of the quiz, perhaps we should assume standard format.

Alternatively — maybe I miscounted? Let me see again.

Actually, looking at the spinner diagram in Q4: It's a circle divided into 6 equal wedges:

Labelled as:

- Red (top)
- Yellow (right)
- Blue (bottom right)
- Red (bottom)
- Green (bottom left)
- Blue (top left)

So yes: Green appears once → 1/6 chance per spin.

Two spins: (1/6)^2 = 1/36

But since no answer choices are listed for Q4 in the provided text, and the user may have forgotten to include them, but based on the problem, the answer is 1/36.

However — wait! Looking back at the original user message — in the image transcription, for Q4, it doesn't show answer choices. But in many such quizzes, sometimes the options are implied or standard.

But since the instruction is to solve accurately, and no options are given for Q4, I will state the correct value.

But hold on — perhaps I made a mistake? Let me check if green is really only one section.

In the spinner for Q4: The labels are:

Starting from top and going clockwise:

1. Red
2. Yellow
3. Blue
4. Red
5. Green
6. Blue

Yes — green is only one section.

So P(green) = 1/6

Two independent spins: (1/6)*(1/6)=1/36

✔ Final Answer for Problem 4: 1/36

But since the user didn’t provide options for Q4, and the other questions had A/B/C/D, perhaps this is an oversight. However, based on math, it’s 1/36.

Wait — let me check if the spinner is different. Maybe “green” is labeled differently? No, according to description, it’s clear.

Alternatively — perhaps the spinner in Q4 is the same as Q1? No, Q1 has 4 sections, Q4 has 6.

Okay, proceeding.

Now, compiling all answers:

Problem 1: D) 1/16
Problem 2: D) 12
Problem 3: C) 4/7 × 3/7
Problem 4: 1/36 (but no options given)

But since the user asked to solve the problems in the image, and for Q4 no options are visible in the text, I’ll provide the calculated answer.

However, upon closer inspection of the user’s input — in the very beginning, it says “10 Questions”, but only 4 are shown. And for Q4, no answer choices are listed in the text provided. So perhaps in the actual image, there are options, but they weren’t transcribed.

To be safe, I’ll assume that for Q4, the expected answer is based on calculation.

But let me think — maybe I misread the spinner. Another possibility: in some spinners, if it’s not specified, but in Q4, the spinner has 6 sections, and green is one, so 1/6.

Perhaps the question is tricking us? No.

Another thought: maybe “landing on green both times” — and if the spinner has more than one green? But from description, only one.

I think 1/36 is correct.

But since the user might expect matching to options, and none are given, I’ll proceed with the math.

Final Answers:

1. D
2. D
3. C
4. 1/36

But for consistency, since Q4 has no options, perhaps the user intends for us to leave it as is.

Wait — looking back at the user’s message: In the image, for Q4, after the question, there are no A/B/C/D listed. Whereas for Q1-Q3, they are. So likely, in the original, Q4 options are missing in transcription.

Given that, and since the task is to solve accurately, I’ll provide the numerical answer for Q4.

But to match the format, perhaps I should note that.

Alternatively — let me check online or standard problems — but no, I must rely on given info.

I think it’s fine.

So, summarizing:

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Final Answer:
1. D
2. D
3. C
4. \frac{1}{36}