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 two jars as Jar A and Jar B.

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

Total marbles in each jar:
- Jar A: 15 marbles
- Jar B: 15 marbles

Ahmad moves 2 blue marbles from Jar A to Jar B.

After the move:
- Jar A: 3 blue marbles and 10 red marbles (total 13 marbles)
- Jar B: 7 blue marbles and 10 red marbles (total 17 marbles)

Next, Ahmad chooses one marble from each jar. We want to find the probability that he selects 2 blue marbles:

1. **Probability of selecting a blue marble from Jar A**:
\[
P(\text{Blue from A}) = \frac{\text{Number of blue marbles in A}}{\text{Total marbles in A}} = \frac{3}{13}
\]

2. **Probability of selecting a blue marble from Jar B**:
\[
P(\text{Blue from B}) = \frac{\text{Number of blue marbles in B}}{\text{Total marbles in B}} = \frac{7}{17}
\]

3. **Probability of selecting blue marbles from both jars**:
\[
P(\text{2 Blues}) = P(\text{Blue from A}) \times P(\text{Blue from B}) = \frac{3}{13} \times \frac{7}{17}
\]

Calculating this:
\[
P(\text{2 Blues}) = \frac{3 \times 7}{13 \times 17} = \frac{21}{221}
\]

To express this probability as a percentage, we calculate:
\[
\frac{21}{221} \approx 0.0950 \quad (\text{which is about } 9.50\%).
\]

Rounding this to the nearest percentage gives us:
\[
\text{Probability} \approx 10\%.
\]

Therefore, the final answer is:

\[
\boxed{10}
\]