Say there are two events A and B, with B Subset A, and you know P(A) and P(B). (

Question

Say there are two events A and B, with B Subset A, and you know P(A) and P(B). (a) What is a simple expression for P(A Intersection B^c), using no more information than just P(A) and P(B)? Show your work by listing intermediate equations or by drawing a Venn diagram. (b) Now say you are testing a piece of software, and define events A = "the software crashes" and B = "the software crashes because of a segmentation fault". In English, what is the event A Intersection B^c? (c) If P(A) = 0.05 (probability of crash) and P(B) = 0.02 (probability of segmentation fault), then what is P(A Intersection B^c)? Use your formula from part (a).

Explanation / Answer

a)P(AnBc) =P(An(1-B))=P(AnU) -P(AnB) =P(A)-P(B) (here U is universal set and as B is a subset of A therefore P(AnB)=P(B))

b) here AnBc  signifies events where the software crashes not because of a segmentation fault.

c) P(AnBc)= P(A)-P(B) =0.05-0.02=0.03

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