$$ P(N $$, then $$ N) $$ (12) $$ P(A $$, then $$ A) $$ (13) $$ P(B $$, then $$ B) $$ A Find each probability if you pick a marble, do not replace it, then pick a second marble ( $$ \mathrm{R}= $$ red; $$ \mathrm{B}= $$ blue; $$ \mathrm{G}= $$ green) $$ \mathbf{P} $$ (blue, then green) (15) $$ P( $$ green, then red) $$ P $$ (green, then green) (17) $$ P $$ (green, then not green) $$ P( $$ red, then blue) (19) $$ P $$ (red, then not blue) $$ P $$ (blue, then blue) (21) $$ P $$ (not blue, then not blue)

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UpStudy AI · Accepted Answer

To find the probabilities of drawing marbles of different colors without replacement, we need to know the total number of marbles of each color. Let's assume the following counts for the marbles:

- $$ R $$: Number of red marbles
- $$ B $$: Number of blue marbles
- $$ G $$: Number of green marbles

Let’s denote:
- Total marbles = $$ T = R + B + G $$

Now, we can calculate the probabilities for each scenario step by step.

1. **Probability of picking a blue marble, then a green marble**:
   $$
   P(\text{blue, then green}) = P(\text{blue}) \times P(\text{green | blue})
   $$
   $$
   P(\text{blue}) = \frac{B}{T}
   $$
   $$
   P(\text{green | blue}) = \frac{G}{T - 1}
   $$
   Therefore,
   $$
   P(\text{blue, then green}) = \frac{B}{T} \times \frac{G}{T - 1}
   $$

2. **Probability of picking a green marble, then a red marble**:
   $$
   P(\text{green, then red}) = P(\text{green}) \times P(\text{red | green})
   $$
   $$
   P(\text{green}) = \frac{G}{T}
   $$
   $$
   P(\text{red | green}) = \frac{R}{T - 1}
   $$
   Therefore,
   $$
   P(\text{green, then red}) = \frac{G}{T} \times \frac{R}{T - 1}
   $$

3. **Probability of picking a green marble, then another green marble**:
   $$
   P(\text{green, then green}) = P(\text{green}) \times P(\text{green | green})
   $$
   $$
   P(\text{green | green}) = \frac{G - 1}{T - 1}
   $$
   Therefore,
   $$
   P(\text{green, then green}) = \frac{G}{T} \times \frac{G - 1}{T - 1}
   $$

4. **Probability of picking a green marble, then not green**:
   $$
   P(\text{green, then not green}) = P(\text{green}) \times P(\text{not green | green})
   $$
   $$
   P(\text{not green | green}) = \frac{B + R}{T - 1}
   $$
   Therefore,
   $$
   P(\text{green, then not green}) = \frac{G}{T} \times \frac{B + R}{T - 1}
   $$

5. **Probability of picking a red marble, then a blue marble**:
   $$
   P(\text{red, then blue}) = P(\text{red}) \times P(\text{blue | red})
   $$
   $$
   P(\text{red}) = \frac{R}{T}
   $$
   $$
   P(\text{blue | red}) = \frac{B}{T - 1}
   $$
   Therefore,
   $$
   P(\text{red, then blue}) = \frac{R}{T} \times \frac{B}{T - 1}
   $$

6. **Probability of picking a red marble, then not blue**:
   $$
   P(\text{red, then not blue}) = P(\text{red}) \times P(\text{not blue | red})
   $$
   $$
   P(\text{not blue | red}) = \frac{R + G}{T - 1}
   $$
   Therefore,
   $$
   P(\text{red, then not blue}) = \frac{R}{T} \times \frac{R + G}{T - 1}
   $$

7. **Probability of picking a blue marble, then another blue marble**:
   $$
   P(\text{blue, then blue}) = P(\text{blue}) \times P(\text{blue | blue})
   $$
   $$
   P(\text{blue | blue}) = \frac{B - 1}{T - 1}
   $$
   Therefore,
   $$
   P(\text{blue, then blue}) = \frac{B}{T} \times \frac{B - 1}{T - 1}
   $$

8. **Probability of picking not blue, then not blue**:
   $$
   P(\text{not blue, then not blue}) = P(\text{not blue}) \times P(\text{not blue | not blue})
   $$
   $$
   P(\text{not blue}) = \frac{R + G}{T}
   $$
   $$
   P(\text{not blue | not blue}) = \frac{R + G - 1}{T - 1}
   $$
   Therefore,
   $$
   P(\text{not blue, then not blue}) = \frac{R + G}{T} \times \frac{R + G - 1}{T - 1}
   $$

Now, you can substitute the values of $$ R $$, $$ B $$, and $$ G $$ into these formulas to find the specific probabilities. If you provide the counts of each color, I can calculate the exact probabilities for you.
To find the probabilities of drawing marbles of different colors without replacement, you need to know the total number of marbles of each color. Use the formulas provided to calculate each probability by substituting the actual counts of red ($$ R $$), blue ($$ B $$), and green ($$ G $$) marbles.

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