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:
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Boys in each grade:
- Freshmen: 10
- Sophomores: 7
- Juniors: 10
- Seniors: 9
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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:
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Probability of picking a senior boy: \[ P(\text{Senior Boy}) = \frac{\text{Number of Senior Boys}}{\text{Total Boys}} = \frac{9}{36} = \frac{1}{4} \]
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Probability of picking a senior girl: \[ P(\text{Senior Girl}) = \frac{\text{Number of Senior Girls}}{\text{Total Girls}} = \frac{7}{35} = \frac{1}{5} \]
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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
1 answer