A jury consists of nine persons who are native-born and three persons who are foreign-born. If two of the jurors are randomly picked for an interview, what is the probability that they will both be foreign-born?

We are tasked with finding the probability that both jurors selected at random from a jury of 12 people (9 native-born and 3 foreign-born) will be foreign-born.

### Step 1: Total number of ways to select two jurors
The total number of jurors is 12. We need to calculate how many different pairs of jurors can be selected from these 12 people. This is done using the combination formula \( \binom{n}{r} \), which gives the number of ways to choose \( r \) objects from \( n \) without regard to the order.

\[
\binom{12}{2} = \frac{12 \times 11}{2 \times 1} = 66
\]

### Step 2: Number of ways to select two foreign-born jurors
Since there are 3 foreign-born jurors, the number of ways to select 2 foreign-born jurors from these 3 is:

\[
\binom{3}{2} = \frac{3 \times 2}{2 \times 1} = 3
\]

### Step 3: Probability of selecting two foreign-born jurors
The probability is the ratio of favorable outcomes (selecting two foreign-born jurors) to the total number of possible outcomes (selecting any two jurors):

\[
P(\text{both foreign-born}) = \frac{\binom{3}{2}}{\binom{12}{2}} = \frac{3}{66} = \frac{1}{22}
\]

Thus, the probability that both selected jurors are foreign-born is \( \frac{1}{22} \).

Would you like further clarification on this, or do you have any other questions?

Here are 5 related questions you might explore:
1. What is the probability that both selected jurors are native-born?
2. What is the probability that one juror is native-born and the other is foreign-born?
3. How does the probability change if the jury has 5 foreign-born jurors instead of 3?
4. What is the probability of selecting at least one foreign-born juror?
5. How would the probability change if we selected 3 jurors instead of 2?

**Tip**: When calculating combinations, remember that the order of selection does not matter.

Explore how to calculate the probability that two randomly selected jurors from a group of 12, consisting of 9 native-born and 3 foreign-born jurors, are both foreign-born. This problem utilizes combination and probability formulas, suitable for Grades 9-12 students.

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