# statistics

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Among a group of students, 24% take both a probability course and a business course, while 14% take neither course. The proportion of students taking the business course exceed by 0.16 the proportion of students taking the probability course. Determine the propoertion of students who are taking the probability course

• statistics -

let the percentage taking the prob course be x
then the percentage taking the bus course is x+16

make a Venn diagram, showing two intersecting circles within a rectangle.
place 14 outside the circles in the rectangle,
place 24 in the intersection of the circles

x + x+16 - 24 + 14 = 100 (had to subtract 24, since the 24 included in the x and in the x+16, but we can count it only once)

2x = 94
x=47

so 46% take the probability course

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