Probability - Free Printable

Let's solve each question step by step based on the images and instructions provided in the worksheet.

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Problem 1: Probability of pulling a black marble

Image Description:
The first bag contains:
- 4 black marbles (solid black)
- 3 white marbles (white with no pattern)

Total marbles = 4 + 3 = 7

Probability of pulling a black marble:
$$
P(\text{black}) = \frac{\text{Number of black marbles}}{\text{Total number of marbles}} = \frac{4}{7}
$$

✔ Answer: $ \frac{4}{7} $

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Problem 2: Probability of pulling a white marble

Image Description:
The second bag contains:
- 1 black marble
- 3 white marbles
- 2 patterned (striped) marbles

Wait — we need to clarify: Are the striped marbles considered "white"? The question asks for white, so we assume only solid white marbles count.

So:
- White marbles = 3
- Black = 1
- Striped = 2

Total = 1 + 3 + 2 = 6

But note: The question is asking for white, so we only count the plain white ones.

$$
P(\text{white}) = \frac{3}{6} = \frac{1}{2}
$$

✔ Answer: $ \frac{1}{2} $

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Problem 3: Probability of pulling a black AND white marble out of the bag

This one is tricky. Let’s look at the third bag:

Image Description:
- 2 black marbles
- 2 white marbles
- 3 striped marbles

Total = 2 + 2 + 3 = 7

Now, the question says: “pulling a black and white marble”

But you can only pull one marble at a time. So it's impossible to pull both a black and a white marble in a single draw.

Therefore, the probability of pulling both in one draw is:

$$
P(\text{black and white}) = 0
$$

Because you can't pick two marbles at once unless specified otherwise.

✔ Answer: $ 0 $

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Bottom Section: Likelihood Questions

#### First jar (red and blue marbles):
- Red marbles: 5
- Blue marbles: 2
- Total: 7

Question: How likely are you to grab a red?

Since there are more red marbles than blue, you're more likely to grab a red.

✔ Answer: More likely

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#### Second jar (purple and green marbles):
- Purple marbles: 9
- Green marbles: 2
- Total: 11

Question: How likely are you to grab a green?

There are fewer green marbles, so you're less likely to grab a green.

✔ Answer: Less likely

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✔ Final Answers:

1. $ \frac{4}{7} $
2. $ \frac{1}{2} $
3. $ 0 $
- (You cannot pull both a black and white marble in one draw)
4. More likely (to grab red)
5. Less likely (to grab green)

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Let me know if you'd like this formatted as a printable answer sheet!