How to do this? (statistic venn diagram question)

Step-by-step explanation:

The probability of A given B, P(A|B), means your universe is only the contents of the circle labeled B. 18 of the 18+72=90 elements in that universe are A elements, so the probability of A given B is 18/90 = 1/5 = 0.200.

__

The probability of B given A, P(B|A), works the same way. For this problem, your universe is only the contents of the circle labeled A. Of the 52+18=70 elements in circle A, 18 of them are B elements. Hence the probability of B given A is 18/70 = 9/35 ≈ 0.257.

__

You get the same result if you use the formula for conditional probability based on the diagram as a whole.

  P(A|B) = P(A&B)/P(B) = (18/(52+18+72+94)) / ((18+72)/(52+18+72+94))

  = 18/(18+72) = 18/90 = 1/5 . . . . same as above.

In like fashion, ...

  P(B|A) = P(A&B)/P(A) = (18/(52+18+72+94)) / ((52+18)/(52+18+72+94))

  = 18/(52+18) = 18/70 = 9/35 . . . . same as above