Can you help me with my last Probability question?

Question by Emperor: Can you help me with my last Probability question?

A large consumer 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
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 the 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 advertisement seems to have had the bigger effect on customer purchases?

Any help is appreciated. Thanks. Free computer help and spanish help if you help me out with this.And your ten points of course.:)
PR squared thank you very much!

Best answer:

Answer by Pi R Squared
Hi,

The probabilities assigned were
P(B)=.20
P(S)=.40
P(B?S)=.12
a.)What is the probability of an individual 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)?

.12 bought out of the .40 who remember seeing the ad.

.12/.40 = 30% bought <==ANSWER When only 30% were persuaded to buy their soap, the company may want to reconsider investing their money in these ads. b.)Assume the 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? 20% is the probability of someone buying their soap, from P(B) = .20. Would you expect that continuing the advertisement will increase the company's market share? Not likely Why or why not? While overall market share was 20%, the 30% of people remembering the ads who bought the soap does show an increase in purchasing, so it was effective. But it could have been a LOT more effective, so I'd explore other ideas. 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? .10/.30 = 33% bought Which advertisement seems to have had the bigger effect on customer purchases? The new ad seems to have a slightly bigger effect on customers. I hope that helps!! :-)

What do you think? Answer below!