Question: In a given population of 100 students 15 are familiar with the statistics software SAS, 35 are familiar with SPSS and 5 students are familiar with both. Use the following Venn diagram and formulas as an aid to answering the problems.

For any randomly chosen individual in this population

(a) P(A) = probability of knowing SAS =

(b) P(B) = probability of knowing SPSS =

(c) P(A intersection B) = probability of knowing both SAS and SPSS =

(d) P(A union B) = probability of knowing SAS or SPSS =

(e) P(A|B) = probability of knowing SAS given that the student knows SPSS =

(f) P(B|A) = probability of knowing SPSS given that the student knows SAS =