Are you good with probability Questions?10 points and more?

Question by Emperor: Are you good with probability Questions?10 points and more?

This is my last problem and I’m not sure how to solve this:
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.That is if you ever need it.And your ten points of course.:)
Thank you Isaac. I appreciate it.

Best answer:

Answer by Isaac N
P[B/S] = P[B and S] / P[S]

This is about all you need to do the problem. For the first question, I got that the probability of an individual purchasing the product given that the individual recalls seeing the advertisement is 0.3.

It’s interesting how you might interpret this result. We know that if a person “recalls” seeing the advertisement, that this increases the probability of the person purchasing the soap from 0.2 to 0.3. However, that does not mean that if a person saw the advertisement that it increases the probability of them purchasing the soap.

There may be people that saw the advertisement and forgot about it. Chances are, this demographic is less likely to purchase the soap because they found its advertisement forgettable. Therefore, it may even out, and the probability of a person purchasing the soap, given that the person has seen the advertisement (regardless of whether they remember it), might not increase.

So the calculations are easy, but interpretation of the results might be complicated.

Personally, I would give the following answers:

Seeing the advertisement does not necessarily increase the probability of the person purchasing the soap. I therefore cannot reccomend whether or not to continue the advertisement.

In the second question, I would estimate the market share to be 20%, assuming that everyone buys soap. If competitors also run advertisements, then it is not clear whether continuing advertisements will increase market share, though it may keep it from decreasing.

In the third question, P[B/S] = 0.33, so it seems that the second advertisement had a bigger effect. However, this is not necessarily the case because we again do not know the behavior of the people who saw the advertisement and forgot about it.

Add your own answer in the comments!