The grades of a freshman college class, obtained after the first year of college, were analyzed.
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# The grades of a freshman college class, obtained after the first year of college, were analyzed. Seventy percent

of the students in the top quarter of the college class had graduated in the upper 10% of their high school class while on 20% of the students in the bottom quarter of the college class had graduated in the upper 10% of their high school class. Of the remaining 50% of the college class (the "middle half") 55% had graduated in the upper 10% of their high school class.

a) Construct a tree diagram to represent this problem.

b) What proportion of the students in the freshman class were in the upper 10% of their high school class?

c) A randomly selected student graduated in the upper 10% of their high school class. What are the probabilities they are in the top quarter, middle half or bottom quarter of their freshman class?

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