The table below gives data on students in a certain school who took the SAT.

	% taking SAT	% who scored over 1000
Seniors	42%	80%
Juniors	30%	66%
Sophomores	11%	56%
Freshmen	17%	47%

The first column of numbers shows what percentage of the total pool of students came from each class. For example, 42% of those taking the SAT were seniors. (Notice that the numbers in this column add up to 100%.) The right column of numbers indicates what percentage of each group scored over 1000. For example, 80% of the Seniors scored over 1000. Use this data to construct a tree diagram similar to the one shown below. Your numbers will differ from those shown. In the tree, H represents those scoring "high" (over 1000) and L represents those scoring "low" (under 1000).Use your tree to answer the following questions.

(a) If you learn that a student (whom you know nothing else about) made over 1000 on the SAT, what then (based on that information) is the conditional probability the student is a senior? (b) If you learn that a student (whom you know nothing else about) made under 1000 on the SAT, what then (based on that information) is the conditional probability the student is a freshman