A sample of 2000 adults were asked whether or not they have ever shopped on the
ID: 3052481 • Letter: A
Question
A sample of 2000 adults were asked whether or not they have ever shopped on the internet. The following table gives a two-way classification of the responses.
a) If an adult is selected at random from these 2000 adults, find the probability that this adult
(i) has never shopped on the internet
(ii) is a male
(iii) has shopped on the internet given that this adult is a female
(iv) is a male given that this adult has never shopped on the internet
(b) Are the events “female” and “have shopped” independent? Why or why not?
Have Shopped Have Never Shopped Male 300 900 Female 200 600Explanation / Answer
Every calculation, with formulae beneath:
(i) has never shopped on the internet
= (900+600)/2000 = .750
(ii) is a male
= (300+900)/2000 = .600
(iii) has shopped on the internet given that this adult is a female
= 200/(200+600) = .250
(iv) is a male given that this adult has never shopped on the internet
= 900/(900+600) = .600
(b) Are the events “female” and “have shopped” independent? Why or why not?
P( female & have shopped) = 200/2000 = .10
P(female) = 800/2000 = .4
P( have shopped) = (200+300)/2000 = .25
P(female)*P(have shopped) = .4*.25 = .10
Since P(female & have shopped) = P(female)*P(have shopped) , Therefore, events "Female" and "have shopped" are independent
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