Question

The table shows the membership in the high school band. HS Band Freshmen Sophomores Juniors Seniors Boys 10 7 10 9 Girls 8 11 9 7 What is the probability that a boy and a girl chosen randomly will both be seniors? (1 point) Responses 14 1 4 15 1 5 19 1 9 120

Answer 1

To find the probability that a randomly chosen boy and girl are both seniors, we first need to determine the total number of boys and girls in the band.

From the table:

- Boys in each grade:
- Freshmen: 10
- Sophomores: 7
- Juniors: 10
- Seniors: 9

- Girls in each grade:
- Freshmen: 8
- Sophomores: 11
- Juniors: 9
- Seniors: 7

Now let's calculate the total number of boys and girls:

**Total Boys:**
\( 10 + 7 + 10 + 9 = 36 \)

**Total Girls:**
\( 8 + 11 + 9 + 7 = 35 \)

Next, we find the number of seniors:

- Number of senior boys = 9
- Number of senior girls = 7

Now we can calculate the probabilities:

1. **Probability of picking a senior boy:**
\[
P(\text{Senior Boy}) = \frac{\text{Number of Senior Boys}}{\text{Total Boys}} = \frac{9}{36} = \frac{1}{4}
\]

2. **Probability of picking a senior girl:**
\[
P(\text{Senior Girl}) = \frac{\text{Number of Senior Girls}}{\text{Total Girls}} = \frac{7}{35} = \frac{1}{5}
\]

3. **Probability of both picking a senior boy and a senior girl:**
Since these events are independent, we can multiply the probabilities:
\[
P(\text{Senior Boy and Senior Girl}) = P(\text{Senior Boy}) \times P(\text{Senior Girl}) = \frac{1}{4} \times \frac{1}{5} = \frac{1}{20}
\]

Thus, the probability that a randomly chosen boy and girl will both be seniors is \(\frac{1}{20}\).

The correct response is:
1/20