Question

In: Statistics and Probability

A company makes TV advertisements to promote its products. Based on the survey results it is...

A company makes TV advertisements to promote its products. Based on the survey results it is known: The chance of someone buying the product is 0.2, the chance someone sees the ad is 0.4, and the chance of someone buying the product and seeing the ad is 0.12.
a. what is the chance someone does not buy the product and see the ad b. what is the chances of someone buying a product if it is known he saw an ad
c. what is the chance for someone to buy the product if it is known he did not see the ad
d. Is the occurrence of a product purchase independent of the incident seeing the ad

Expert Solution

P[ someone buying the product ] =0.2

P[ someone sees the ad ] = 0.4

P[ someone buying the product and seeing the ad ] = 0.12

a. what is the chance someone does not buy the product and see the ad

P[ someone does not buy the product and see the ad ] = P[ someone sees the ad ] - P[ someone buying the product and seeing the ad ]

P[ someone does not buy the product and see the ad ] = 0.4 - 0.12

P[ someone does not buy the product and see the ad ] = 0.28

b. what is the chances of someone buying a product if it is known he saw an ad

P[ buying a product if it is known he saw an ad ]= P[ buying a product | someone sees the ad ]

P[ buying a product | someone sees the ad ] = P[ someone buying the product and seeing the ad ] /P[ someone sees the ad ]

P[ buying a product | someone sees the ad ] = 0.12/0.4

P[ buying a product | someone sees the ad ] = 0.3

c. what is the chance for someone to buy the product if it is known he did not see the ad

P[ someone buying the product and did not seeing the ad ] = P[ someone buying the product ] - P[ someone buying the product and seeing the ad ]

P[ someone buying the product and did not seeing the ad ] = 0.2 - 0.12

P[ someone buying the product and did not seeing the ad ] = 0.08

P[ someone did not see the ad ] = 1 - P[ someone sees the ad ] = 1 - 0.4 = 0.6

P[ someone buying the product given did not seeing the ad ] =P[ someone buying the product and did not seeing the ad ] / P[ someone did not see the ad ]= 0.08/0.6

P[ someone buying the product given did not seeing the ad ] = 0.133

d. Is the occurrence of a product purchase independent of the incident seeing the ad

P[ someone buying the product given did not seeing the ad ] is not equal to P[ someone buying the product ]

Hence are not independent

orchestra answered 2 years ago

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