Question

Randomly select a painted rock from a bag containing
4
4 purple rocks,
3
3 green rocks,
3
3 orange rocks, and
2
2 blue rocks. Do not simplify your ratio.





Outcome Purple Green Orange Blue
Probability
4


3


3


2

Is this a Uniform Probability Model


yes
Randomly select a painted rock from a bag containing
4
4 purple rocks,
3
3 green rocks,
3
3 orange rocks, and
2
2 blue rocks. Do not simplify your ratio.





Outcome Purple Green Orange Blue
Probability
4


3


3


2

Is this a Uniform Probability Model


yes
Randomly select a painted rock from a bag containing
4
4 purple rocks,
3
3 green rocks,
3
3 orange rocks, and
2
2 blue rocks. Do not simplify your ratio.





Outcome Purple Green Orange Blue
Probability
4


3


3


2

Is this a Uniform Probability Model


yes

Answer 1

To determine if this scenario represents a Uniform Probability Model, we need to examine the probabilities associated with each outcome.

A Uniform Probability Model is one where all outcomes have the same probability. In your case, the outcomes and their respective counts are:

- Purple: 4
- Green: 3
- Orange: 3
- Blue: 2

The total number of rocks is \(4 + 3 + 3 + 2 = 12\).

Now, let's write down the probability of each color of rock:

- Probability of selecting a Purple rock: \( \frac{4}{12} \)
- Probability of selecting a Green rock: \( \frac{3}{12} \)
- Probability of selecting an Orange rock: \( \frac{3}{12} \)
- Probability of selecting a Blue rock: \( \frac{2}{12} \)

These probabilities simplify to:

- Purple: \( \frac{1}{3} \)
- Green: \( \frac{1}{4} \)
- Orange: \( \frac{1}{4} \)
- Blue: \( \frac{1}{6} \)

Since the probabilities associated with each outcome are not equal (e.g., \( \frac{1}{3} \) for Purple is not equal to \( \frac{1}{4} \) for Green/Orange or \( \frac{1}{6} \) for Blue), this is **not** a Uniform Probability Model.

Therefore, the answer is:

No, this is not a Uniform Probability Model.