Of the 300 subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subject experienced exactly two of these effects, how many subjects experienced only one of these effects?
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SONIKA VASANTH
From the question WKT 40% experienced wetting and 30% experienced vomiting
So it should be A+B. I dint understand why it is A +B+C
Total=A+B+C-(AnB+AnC+BnC)(or Exactly 2-group overlaps)- 2*(AnBnC)+Neither
As I mentioned before, we need to subtract 2(AnBnCn) in order to account for the over-counting of this group. Someone in this group experiences all of the symptoms and is therefore counted in the groups A, B, and C. However, a subject in the group (AnBnC) is really only one individual, so we should only be counting the subject once. To account for the over-counting, we subtract 2 of the 3 times the subject was counted as a part of the various groups. That way, we only count subjects in the group (AnBnC) once :)
Good question :) In the explanation above, Misagh used the formula for three overlapping sets:
Total = A + B + C - (AnB+AnC+BnC) - 2*(AnBnC) + Neither
where (AnB+AnC+BnC) is the sum of 2-group overlaps and (AnBnC) represents subjects with all three symptoms.
For the term 2*(AnBnC), we can think about why we need to subtract 2*(all three) in the following way: if a subject experiences all three symptoms, the subject will be counted 3 different times (once for A, once for B, and once for C.) However, we are still only talking about 1 subject. Since he is represented 3 times, we need to subtract the two extra times that he was counted.
300*40/100= 120 sweaty palms
300*30/100=90 vomiting
300*75/100=225 dizziness
300*35/100=105 (35%subjects experienced exactly two of these effects)
Neither=0
At first we need to find overlapping between 3 groups(AnBnC):
3 Explanations