Let ?A ?denote the event that the next request for assistance from a statistical software consultant relates to the SPSS package, and let ?B ?be the event that the next request is for help with SAS. Suppose that P(A) =. 30 and P(B) = .50. a. Why is it not the case that P(A) + (B) = 1? b. Calculate P(A ?) . c. Calculate P(A ?B). d.Calculate P(A? ?B?).

Answer : Step 1 : Let A denote the event that the next request for assistance from a statistical software consultant relates to the SPSS package, and let B be the event that the next request is for help with SAS. Suppose that P(A) =. 30 and P(B) = .50. a). There are other packages like SPSS and SAS. There are a variety of programs which are like SPSS and SAS. Step 2 : b). We have to calculate P(A ) . We know that P (A) = 0.30 So P(A’)=1- P(A) P(A’)=1- P(A) P(A’)=1- 0.30 P(A’)=0.7