Counting and Probability: Determine product efficacy

[logicaljoe]

Three drugs: A, B and C

50 subjects reported relief from:

21 drug a
21 drug b
31 drug c

9 a&b
14 a&c
15 b&c

41 report relief from at least one drug

Note that some of the subjects who reported results from A might have done so for B and C etc.

a. How many got relief from none of the drugs?

I assume I use the difference rule here

50 - 41 = 9 subjects that didn't report any relief.

b. How many people got relief from all 3 drugs?

D[A intersection B intersection C] = 21 + 21 + 31 - 9 - 14 - 15 = 35

such that 41 - 35 = 6 The number of subjects relieved by all three drugs.

c. How many subjects got relief from A only?

I'm kind of unsure about this question.

D[A - (A intersection B) - (A intersection C)]

So how do I identify the specific users that have ticked in both a int b and a int c?

21 - 9 - 14 + 6 = 4

This is all I can think off.

 

[EnumaElish]

Your answer to c is correct, except the formula should be D[A - (A intersection B) - (A intersection C) + (A intersect. B intersect. C)].