6. Two thousand randomly selected adults were asked whether or not they have eve
ID: 2946097 • Letter: 6
Question
6. Two thousand randomly selected 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 500 300 Have Never Shopped 700 500 Male Female If one adult is selected at random from these 2000 adults, find the probability that this adult i. has never shopped on the Internet. 11, 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 v. Are the event male and female mutually exclusive? vi. Are the event male and have shopped mutually exclusive? (Hint: first step- find total number of male, total number of female, total number of people who have shopped and total number of people who have never shopped online.)Explanation / Answer
Total people = 2000
a) Probability that an adult has never shopped on internet is computed as:
= 1200 / 2000
= 0.6
Therefore 0.6 is the required probability here.
b) Probability that the adult is a male
= 1200 / 2000
= 0.6
Therefore 0.6 is the required probability here.
c) Given that the person is female, probability that she has shopped on the internet is computed as:
= 300 / 800
= 0.375
Therefore 0.375 is the required probability here.
d) Given that the adult has never shopped on internet, probability that the adult is a male is computed as:
= 700 / 1200
= 0.5833
Therefore 0.5833 is the required probability here.
e) Clearly an adult can be only female or male, cannot be both, therefore the two events are mutually exclusive.
f) Clearly P( male and have shopped ) is not equal to 0, therefore the two events here are not mutually exclusive.
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