Last Updated on May 3, 2023
Of the 300 subjects who participated in an experiment using…
Solution:
This is a 3-circle Venn Diagram problem. Because we do not know the number of unique items in this particular set, we can use the following formula:
Total # of Unique Elements = # in (Group A) + # in (Group B) + # in (Group C) – # in (Groups of Exactly Two) – 2 [#in (Group of Exactly Three)] + # in (Neither)
Next we can label our groups with the information presented.
number in Group A = # who experienced sweaty palms
number in Group B = # who experienced vomiting
number in Group C = # who experienced dizziness
We are given that 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.
We can solve for the number in each group:
number who experienced sweaty palms = 300 x 0.4 = 120
number who experienced vomiting = 300 x 0.3 = 90
number who experienced dizziness = 300 x 0.75 = 225
We are also given that all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects.
This means the following:
number in Groups of Exactly Two = 300 x 0.35 = 105
Since all the subjects experienced at least one of the effects it means that the # in (Neither) is equal to zero. We can now plug in all the information we have into our formula, in which T represents # in (Group of Exactly Three).
Total # of Unique Elements = # in (Group A) + # in (Group B) + # in (Group C) – # in (Groups of Exactly Two) – 2 [#in (Group of Exactly Three)] + # in (Neither)
300 = 120 + 90 + 225 – 105 – 2T + 0
300 = 330 – 2T
30 = 2T
15 = T
Now that we have determined a value for T, we are very close to finishing the problem. The question asks how many of the subjects experienced only one of these effects.
To determine this we can set up one final formula.
Total = # who experienced only 1 effect + # who experienced two effects + # who experienced all 3 effects + # who experienced no effects
We can let x represent the # who only experienced 1 effect.
300 = x + 105 + 15 + 0
300 = x + 120
180 = x
Answer: D
