Hi Jaheim.
First, convert the problem into equations.
Recall percentages can be expressed as decimals, and let's use F for first year students and U for upper-class students. So 45%=.45, 35% = .35 and so on.
If 45% attend, and 64% of that 45% are U, then (.6$)*(.45)=.288. Meaning 28.8% of the total student body are attending who are U. Easy to get confused here, not saying 28.8% of U are attending. Saying that 28.8% of total students attend who happen to also be U.
The same for not attending. 55% don't attend regularly (100%-45%). 34% of them are U. 34% of 55% is (.34)*(.55) = .187. So 18.7% of the total student body who are U, do not attend. Again, that's not 18.7% of U, an easy mistake to make. It's 18.7% of total student body who are also U.
Since 28.8% of the students are U who DO attend, and 18.7% are U who DO NOT attend, U represents (.288+.187=.475) 47.5% of the total student body. This is the U total relative to total student population.
For the actual question, a randomly selected U, what are the odds they will attend? Well we need a ratio. Those that do attend over the total. Let's take that (.288) and put it over (.475). Because probability of attending is those who do out of the total.
(.288)/(.475) = .6063 (rounded). Meaning, 60.63% of Upper Class students regularly attend. That's the answer for this particular problem.
Hope you found this helpful not just for the answer but the logic in how to reach it. Avoid the common pitfall of thinking the percent of a percent represents the total for just Upper class.
Regards,
Michael
