Certainly! Let's solve the given problem step-by-step to find the probability that an applicant planning to stay off-campus is a transfer applicant.
1. Identify the given data:
- Number of transfer applicants who plan to live off-campus: [tex]\( 66 \)[/tex]
- Total number of applicants who plan to live off-campus: [tex]\( 118 \)[/tex]
2. Define the probability formula:
The probability [tex]\( P \)[/tex] that an applicant planning to stay off-campus is a transfer applicant is given by:
[tex]\[
P(\text{Transfer} | \text{Off-Campus}) = \frac{\text{Number of transfer applicants planning to live off-campus}}{\text{Total number of applicants planning to live off-campus}}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
P(\text{Transfer} | \text{Off-Campus}) = \frac{66}{118}
\][/tex]
4. Calculate the probability:
[tex]\[
P(\text{Transfer} | \text{Off-Campus}) \approx 0.559
\][/tex]
5. Match the calculated probability with the given choices:
The calculated probability [tex]\( 0.559 \)[/tex] matches choice B.
Therefore, the probability that an applicant planning to stay off-campus is a transfer applicant is:
[tex]\[
\boxed{0.559}
\][/tex]
