To find the probability that an applicant planning to stay off-campus is a transfer applicant, we can follow these steps:
1. Identify the number of transfer applicants who plan to stay off-campus.
2. Identify the total number of applicants who plan to stay off-campus.
3. Use these values to calculate the probability.
Given the two-way frequency table:
[tex]\[
\begin{array}{|l|c|c|c|}
\hline
& \text{On-Campus} & \text{Off-Campus} & \text{Total} \\
\hline
\text{Transfer Applicants} & 38 & 66 & 104 \\
\hline
\text{Freshman Applicants} & 85 & 52 & 137 \\
\hline
\text{Total} & 123 & 118 & 241 \\
\hline
\end{array}
\][/tex]
1. The number of transfer applicants who plan to stay off-campus is 66.
2. The total number of applicants who plan to stay off-campus is 118.
Now the probability [tex]\( P(\text{Transfer Applicant}|\text{Off-Campus}) \)[/tex] is given by the ratio of transfer applicants staying off-campus to the total number of off-campus applicants:
[tex]\[
P(\text{Transfer Applicant}|\text{Off-Campus}) = \frac{\text{Number of Transfer Applicants staying Off-Campus}}{\text{Total Number of Off-Campus Applicants}}
\][/tex]
Substituting the values:
[tex]\[
P(\text{Transfer Applicant}|\text{Off-Campus}) = \frac{66}{118}
\][/tex]
Perform the division to find the probability:
[tex]\[
P(\text{Transfer Applicant}|\text{Off-Campus}) \approx 0.559
\][/tex]
So, the probability that an applicant planning to stay off-campus is a transfer applicant is approximately 0.559. Therefore, the correct answer is:
B. 0.559
