Consider the following cross-tabulation table of brand preference for digital cameras and their primary usage (professional or personal):

Usage

Digitalcamerabrandpreference

Total

Canon

Nikon

Pentax

Professional

Personal

48

30

15

95

27

65

90

190

78

110

92

280

Total

(a)What is the probability of randomly selecting a professional user?

(b)What is the probability of selecting a user who prefers the Nikon brand?

(c)Find the probability that a user prefers the Pentax brandgiventhat their usage is primarily personal.

(d)Is brand preference statistically independent of primary usage? Justify your answer with a statistical illustration and explain the meaning of your finding.

(e)What is the likelihood that a randomly selected user prefers the Canon brand and is a professional user?

(f)Find the probability of randomly selecting either a professional user or a user who prefers the Nikon brand of digital camera or both.

(g)Are the two events primary usage and brand preference mutually exclusive? Justify your answer statistically.