A journal article reported in September 2003 that a Swiss de

A journal article reported in September 2003 that a Swiss dermatologist established a link between smoking and gray hair in women under 40, with results as shown in this table. Let G denote the event a women in the study has gray hair, and S denote the event a women in the study is a smoker.

a) Was this an observational study or an experiment?

b) Find P(G)

c) Find P(S or G)

d) Find P(S|G)

e) Are having Gray hair and being a smoker independent or dependent events? Explain.

Solution

a)
Observational study
b)
P(G) = n( Has grow Hair) / N(Total) = 13/55 = 0.2364
c)
P(S or G) = P(S) + P(G) - P(S n G) = 23/55 + 13/55 - 13/55 = 23/55 = 0.4181
d)
P(S|G) = P( S n G) / P(S) = (13/55)/ (23/55) = 13/23 = 0.5652
e)
dependent events , because P( S n G) != P(S) * P(G)