A sample of 2000 adults were asked whether or not they have ever shopped on the

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.

Have Shopped Have Never Shopped

Male 300 900

Female 200 600

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?

Present formulas.

Explanation / Answer

a)i) P(never shop on the internet) = (900 + 600)/2000 = 1500/2000 = 0.75

ii) P(male) = (300 + 900)/2000 = 1200/2000 = 0.6

iii) P(shopped on the internet | female) = P(shopped on the internet and female)/P(female)

                                                              = 200/(200 + 600) = 0.25

iv) P(male | never shopped on internet) = P(male and never shopped on internet)/P( never shopped on internet)

                                                                = 900/1500 = 0.6

b) P(female and have shopped) = 200/2000 = 0.1

P(female) *P( have shopped) = 800/2000 * 500/2000 = 0.1

As P(female and have shopped) = P(female) *P( have shopped) , so these two events are independent.

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