Two thousand randomly selected adults were asked whether or not they have ever s
ID: 3044247 • Letter: T
Question
Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a classification of the responses.
Have Shopped
Have Never Shopped
Total
Male
500
700
1200
Female
300
500
800
Total
800
1200
2000
1. If one adult is selected at random from these 2000 adults. Find the probability that this adult
a. has never shopped on the internet
b. is a male
c. has shopped on the internet given that this adult is a female
d. is a male given that this adult has never shopped on the internet
e. has never shopped on the internet and is a male
f. has shopped on the internet and is a female
g. has never shopped on the internet or is a female
h. is a male or has shopped on the internet
I. has shopped on the internet or has never shopped on the internet.
2. Are the events “male” and “female” mutually exclusive?
What about the events “have shopped” and “male”? Why or why not?
3. Are the events “female” and “have shopped” independent? Why or why not?
Have Shopped
Have Never Shopped
Total
Male
500
700
1200
Female
300
500
800
Total
800
1200
2000
Explanation / Answer
a) probability that this adult has never shopped on the internet =1200/2000 =0.6
b) P( is a male) =1200/2000 =0.6
c)P(has shopped on the internet given that this adult is a female)=300/800 =3/8 =0.375
d)
P( is a male given that this adult has never shopped on the internet) =700/1200 =7/12 =0.5833
e)P(has never shopped on the internet and is a male)=700/2000=7/20=0.35
f) P(has shopped on the internet and is a female)= 300/2000=0.15
g) P (has never shopped on the internet or is a female) =(300+500+700)/2000 =1500/2000=3/4 =0.75
h) P( is a male or has shopped on the internet) =(500+300+700)/2000 =1500/2000=3/4 =0.75
i)P( has shopped on the internet or has never shopped on the internet)=(800+1200)/2000 =1
2)
YEs events “male” and “female” are mutually exclusive cause they contian no common events.
“have shopped” and “male” are not mutually exclusive cause they contain 500 common events.
3) P(female and shopped) =300/2000=0.15
P(female)*P(shopped) =(800/2000)*(800/2000)=0.4*0.4 =0.16
as P(female)*P(shopped) is not equal to P(female and shopped) ; threfore events “female” and “have shopped” are not independent.
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