Question

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)=0.30 and P(B) = 0.50.

(a) Why is it not the case that P(A) + P(B) = 1?

(b) Calculate P(A').

(c) Calculate P(A \( \cup \)B).

(d) Calculate P(A' \( \cap \)B').

Answer 1

solution

We have P(A)=0.30 and P(B)=0.50

(a) Why is it not the case that P(A) + P(B) = 1?

since there is another service so A and B is not the complement event so , P(A)+P(B) \( \neq \)1

(b) Calculate P(A').

=>P(A')=1-P(A)=1-0.30=0.7

(c) Calculate P(A \( \cup \)B).

=>P(A\( \cup \)B)=P(A)+P(B)=0.30+0.50=.08

(d) Calculate P(A'\( \cap \)B').

=>P(A' \( \cap \)B')=P(\( \overline{A\cup B} \))=1-P(A\( \cup \))

                   =1-0.8=0.2

Answer

(a), So, P(A)+P(B)\( \neq \)1

(b). P(A')=0.7

(c). P(A\( \cup \)B)=0.8

(d). P(A'\( \cap \)B')=0.2