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.

Question
To the nearest percentage, what is the probability that Ahmad selects 2 blue marbles? Enter the answer in the box.

Response area with 1 text input box
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Answer 1

Let's break down the situation step by step.

Initially, both jars contain:
- Jar 1: 5 blue marbles, 10 red marbles
- Jar 2: 5 blue marbles, 10 red marbles

After Ahmad moves 2 blue marbles from Jar 1 to Jar 2, the distribution of marbles becomes:
- Jar 1: 3 blue marbles, 10 red marbles
- Jar 2: 7 blue marbles, 10 red marbles

Next, we will calculate the probabilities of selecting a blue marble from each jar.

**Probability of selecting a blue marble from Jar 1:**
- Total marbles in Jar 1 = 3 blue + 10 red = 13 marbles
- Probability (Jar 1) = Number of blue marbles in Jar 1 / Total marbles in Jar 1
\[
P(\text{blue from Jar 1}) = \frac{3}{13}
\]

**Probability of selecting a blue marble from Jar 2:**
- Total marbles in Jar 2 = 7 blue + 10 red = 17 marbles
- Probability (Jar 2) = Number of blue marbles in Jar 2 / Total marbles in Jar 2
\[
P(\text{blue from Jar 2}) = \frac{7}{17}
\]

**Now, we find the probability of selecting 2 blue marbles (1 from each jar):**
The events are independent, so we multiply the probabilities:
\[
P(\text{both blue}) = P(\text{blue from Jar 1}) \times P(\text{blue from Jar 2}) = \frac{3}{13} \times \frac{7}{17}
\]

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

Now, we convert this probability to a percentage:
\[
\frac{21}{221} \approx 0.0950 \text{ or } 9.50\%
\]

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

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