A large consumer goods company ran a television advertisement for one of its soap products.
On the basis of a survey that was conducted, probabilities were assigned to the following
events.
B = individual purchased the product S = individual recalls seeing the advertisement B∩S = individual purchased the product and recalls seeing the advertisement

The probabilities assigned were P(B)=.20,P(S)=.40, and P(B∩S)=.12

a. What is the probability of an individual’s purchasing the product given that the individual
recalls seeing the advertisement? Does seeing the advertisement increase
the probability that the individual will purchase the product? As a decision maker,
would you recommend continuing the advertisement (assuming that the cost is
reasonable)?
b. Assume that individuals who do not purchase the company’s soap product buy from
its competitors. What would be your estimate of the company’s market share? Would
you expect that continuing the advertisement will increase the company’s market
share? Why or why not?
"c. The company also tested another advertisement and assigned it values of P(S)=.30
and P(B∩S)=.10. What is P(B|S) for this other advertisement? Which advertise-
ment seems to have had the bigger effect on customer purchases?"

B = individual purchased the product S = individual recalls seeing the advertisement B∩S = individual purchased the product and recalls seeing the advertisement

The probabilities assigned were P(B)=.20,P(S)=.40, and P(B∩S)=.12

a) P(B/S) = [tex]\frac{P(B\bigcap S}{P(S)} \\=\frac{0.12}{0.40} \\=0.30[/tex]

Yes we can continue the advt since P(B/A) >P(B)

b)

It is preferable to continue advt as chances of purchase after seeing advt is more than purchase without seeing advt.

c) P(B/S) =[tex]\frac{P(B\bigcap S}{P(S)} \\=\frac{0.1}{0.3} \\=0.3333[/tex]

The II advt has the bigger effect since conditional prob is more here.