Question

Two jars each contain 5 blue and 10 red marbles. Ahmad moves 2 blue marbles from one jar to the other jar. Ahmad then randomly selects 1 marble from each jar.
To the nearest percentage, what is the probability that Ahmad selects 2 blue marbles? Enter the answer in the box.

Answer 1

Let's denote the jars as Jar A and Jar B.

Initially:
- Jar A: 5 blue and 10 red marbles
- Jar B: 5 blue and 10 red marbles

After Ahmad moves 2 blue marbles from Jar A to Jar B:
- Jar A: 3 blue and 10 red marbles (5 - 2 = 3)
- Jar B: 7 blue and 10 red marbles (5 + 2 = 7)

Next, we need to find the probability that Ahmad selects 1 blue marble from each jar.

1. **Calculate the probability of selecting a blue marble from Jar A:**
- Total marbles in Jar A = 3 blue + 10 red = 13 marbles
- Probability of selecting a blue marble from Jar A = \( \frac{3}{13} \)

2. **Calculate the probability of selecting a blue marble from Jar B:**
- Total marbles in Jar B = 7 blue + 10 red = 17 marbles
- Probability of selecting a blue marble from Jar B = \( \frac{7}{17} \)

3. **Calculate the combined probability of selecting a blue marble from both jars:**
- Probability of selecting 1 blue marble from Jar A and 1 blue marble from Jar B =
\[
\left(\frac{3}{13}\right) \times \left(\frac{7}{17}\right)
\]

Now we compute that:
\[
\text{Combined probability} = \frac{3 \times 7}{13 \times 17} = \frac{21}{221}
\]

4. **Convert the probability to percentage:**
\[
\text{Percentage} = \left(\frac{21}{221}\right) \times 100 \approx 9.50\%
\]
Rounding this to the nearest percentage gives us 10%.

Thus, the final answer is:
\[
\boxed{10}
\]