Question

Consider a jar that has 18 marbles. There are 5 red, 7 blue, and 6 green marbles. What is the probability of selecting a red marble and then, without replacing it, selecting a green marble? Enter your response as a decimal rounded to the nearest thousandth.(1 point)

Answer 1

To find the probability of selecting a red marble and then a green marble without replacement, we can follow these steps:

1. **Calculate the probability of selecting a red marble first:**
There are 5 red marbles out of a total of 18 marbles. Thus, the probability of selecting a red marble is:
\[
P(\text{Red}) = \frac{5}{18}
\]

2. **Calculate the probability of selecting a green marble after a red marble has been selected:**
After selecting a red marble, there will now be 17 marbles left in total (since we do not replace the red marble), and there are still 6 green marbles. Thus, the probability of selecting a green marble after selecting a red marble is:
\[
P(\text{Green | Red}) = \frac{6}{17}
\]

3. **Calculate the combined probability of both events happening:**
Since the events are dependent, we multiply the probabilities:
\[
P(\text{Red and then Green}) = P(\text{Red}) \times P(\text{Green | Red}) = \frac{5}{18} \times \frac{6}{17}
\]

Now doing the multiplication:
\[
P(\text{Red and then Green}) = \frac{5 \times 6}{18 \times 17} = \frac{30}{306}
\]

4. **Simplifying the fraction:**
We can simplify the fraction \(\frac{30}{306}\). The greatest common divisor of 30 and 306 is 6. Therefore:
\[
\frac{30 \div 6}{306 \div 6} = \frac{5}{51}
\]

5. **Convert the fraction into a decimal:**
To convert \(\frac{5}{51}\) into a decimal:
\[
5 \div 51 \approx 0.0980392
\]

6. **Round to the nearest thousandth:**
Rounding \(0.0980392\) to the nearest thousandth gives:
\[
0.098
\]

Thus, the probability of selecting a red marble and then a green marble without replacement, rounded to the nearest thousandth, is:
\[
\boxed{0.098}
\]