To find the probability that the student selected is a girl given that they are a senior, we are looking for [tex]\( P(\text{Girl} \mid \text{Senior}) \)[/tex].
We can start by identifying the relevant information from the table:
1. The total number of seniors.
2. The number of girl seniors.
From the table, the number of seniors can be calculated as follows:
- Number of boy seniors: 5
- Number of girl seniors: 2
Thus, the total number of seniors:
[tex]\[ 5 \text{ (boy seniors)} + 2 \text{ (girl seniors)} = 7 \text{ seniors} \][/tex]
Next, we focus on the number of girl seniors which is given as:
[tex]\[ 2 \text{ girl seniors} \][/tex]
The probability that the student selected is a girl given that they are senior is calculated by:
[tex]\[ P(\text{Girl} \mid \text{Senior}) = \frac{\text{Number of girl seniors}}{\text{Total number of seniors}} \][/tex]
Substituting the identified values:
[tex]\[ P(\text{Girl} \mid \text{Senior}) = \frac{2}{7} \][/tex]
To summarize, the probability that a randomly selected student is a girl given that they are a senior is:
[tex]\[ \frac{2}{7} \approx 0.2857 \][/tex]
Thus, the probability is approximately [tex]\( 0.2857 \)[/tex] or [tex]\( 28.57\% \)[/tex].
