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

Question

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

% taking SAT

% who scored over 1000

45%

79%

30%

70%

10%

58%

15%

48%

The first column of numbers shows what percentage of the total pool of students came from each class. For example, 45% 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, 79% 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?

% taking SAT

% who scored over 1000

Seniors

45%

79%

Juniors

30%

70%

Sophomores

10%

58%

Freshmen

15%

48%

Explanation / Answer

a) if student made over 1000 then probabiluty that he is a senior is

0.78 * 0.47 = 0.3666 or 36.66%

b) student made under 1000 then probability that he is a freshman is

0.52* 0.08 = 0.0416 or 4.16%

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