Question 1: Without replacement, what is the probability of picking a red gummy bear first and then a green gummy bear second?

To calculate the probability of picking a red gummy bear first and a green gummy bear second without replacement, we need two pieces of information:

1. The total number of gummy bears in the set.
2. The number of red and green gummy bears in the set.

Once we have these, the probability can be calculated in two steps:

### Step 1: Probability of picking a red gummy bear first
Let’s assume:
- There are \( N \) total gummy bears.
- \( R \) represents the number of red gummy bears.
- \( G \) represents the number of green gummy bears.

The probability of picking a red gummy bear first is:
\[
P(\text{Red first}) = \frac{R}{N}
\]

### Step 2: Probability of picking a green gummy bear second (after the red one)
Since the red gummy bear has been removed (without replacement), there are now \( N-1 \) gummy bears left. The number of green gummy bears remains \( G \), so the probability of picking a green gummy bear second is:
\[
P(\text{Green second}) = \frac{G}{N-1}
\]

### Step 3: Multiply the probabilities
Since these are independent events, the total probability is the product of both probabilities:
\[
P(\text{Red then Green}) = \frac{R}{N} \times \frac{G}{N-1}
\]

To finalize the calculation, you would need the exact values of \( N \), \( R \), and \( G \).

Would you like me to proceed with a specific number of red, green, and total gummy bears, or clarify further?

Here are some related questions to explore:
1. What if the number of red and green gummy bears were equal?
2. How does the probability change if we allow replacement?
3. What is the probability of drawing two red gummy bears in a row without replacement?
4. How would this change if we had three draws and wanted the first two to be red and the third to be green?
5. What if there are other colors of gummy bears in the bag as well?

**Tip:** When calculating probabilities for events without replacement, always adjust the total count for the second event!

Calculate the probability of selecting a red gummy bear first and a green gummy bear second without replacement. Learn how to apply the multiplication rule for dependent events with clear formulas. Suitable for students in Grades 9-11.

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