Final answer:
To answer the question about the total number of professional schools and liberal arts colleges, precise and current data is necessary. From the provided information, we know the percentage of PhDs out of all degrees in the 2009-2010 academic year and the mutually exclusive nature of post-high school plans.
Step-by-step explanation:
The question regarding the number of total professional schools and liberal arts colleges is difficult to answer precisely without current data, which is not provided here. However, I can address the specific data points mentioned. Regarding the information about degrees awarded in the 2009-2010 academic year, the fraction of PhD degrees awarded among the total (48,069 PhD degrees out of 2,354,678 total degrees) is approximately 2.04 percent. This is computed by dividing the number of PhD degrees by the total number of degrees and then multiplying by 100 to get the percentage.
Events such as attending college, working full-time, and taking a gap year after high school, as mentioned in the question about a class of 300 students, are indeed mutually exclusive because a single student cannot simultaneously attend college and work full-time or take a gap year.
The value and focus of a liberal arts education is generally well-rounded, providing students with broad knowledge across various disciplines, as opposed to a professional school that focuses on specialized skills for a specific career path.