Question

17. 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) + P(B) = 1?
b. Calculate P(A?).
c. Calculate P(A U B).
d. Calculate P(A? intersection B?) .

Answer 1

a. The probability is not equal to 1

b. P (A') = 0.70

c. P ( A U B ) = 0.80

d. P ( A' ∩ B' ) = 0.20

Explanation:

a. Because these A and B are disjoint

b. since the probability of A is 0.30 then the probability of A compliment is

P(A compliment ) = 1 - P (A)

P(A compliment ) = 1-0.30

P(A compliment ) = 0.70

c. Since event are disjoint then intersection of A and B is 0, so probability of A U B is;

P ( A U B ) = P (A) + P(B) - P(A∩ B)

P ( A U B ) = 0.30 + 0.50 - 0

P ( A U B ) = 0.80

d. The inetrsection of compilments of A and B are:

by using De Morgan's Law we have,

P ( A' ∩ B' ) = P [(A U B )']

P ( A' ∩ B' ) = 1 - P ( A U B )

P ( A' ∩ B' ) = 1 - 0.80

P ( A' ∩ B' ) = 0.20