Question 1125388: 1) A retail outlet wanted to know whether its weekly advertisement in the daily newspaper works. To acquire this critical information, the store manager surveyed the people who enter the store and determined whether each individual saw the ad and whether a purchase was made. From the information developed, the manager produced the following table of joint probabilities.
Purchase Status
Purchase No Purchase Total
See the ads 0.22 0.33 0.55
Do not see ads 0.09 0.36 0.45
Total 0.31 0.69 1.00
What is the probability that the customer purchase?
What is the probability that the customer purchase if he sees the ads?
Are the events of “See the Ads” and “Purchase” independent? Show why or why not.
Are the ads effective? Explain
Thanks alot
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Define the two events:
A = person sees advertisement
B = person buys product
What is the probability that the customer purchase?
P(B) = probability of making purchase
P(B) = 0.31 because this is the total in the "purchase" column. This means 31% of people bought the product; therefore the chances of making a purchase is 0.31 or 31%
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What is the probability that the customer purchase if he sees the ads?
P(B|A) = probability of making purchase given they have seen the ad
P(B|A) = P(B and A)/P(B)
P(B|A) = 0.22/0.31 The value 0.22 is in the "buys product" column and "sees ad" row
P(B|A) = 0.709677
If the customer sees the ad, then the probability is approximately 0.709677
Note how the probability changes based on the prior knowledge of seeing the advertisement.
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Are the events of “See the Ads” and “Purchase” independent? Show why or why not.
Since P(B) = 0.31 and P(B|A) = 0.709677, this means that P(B|A) = P(B) is not a true equation. Therefore, A and B are not independent events. We consider them to be dependent events.
If A and B were independent, then both of the following equations would be true
P(A|B) = P(A)
P(B|A) = P(B)
Writing
P(B|A) = P(B)
means that event A has no effect on event B, so the probabilities would not alter. However, P(B) changes once we know that event A happens.
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Are the ads effective? Explain
Yes the advertising is effective. At first, P(B) = 0.31 which is fairly low. Then P(B) jumps up to 0.709677 when we compute P(B|A) = 0.709677
Another way to think of P(B|A) is to break it down into "P(B) given that event A has occurred". So after we know the person saw the ad, the chances of them buying the product is about 71%, which is quite the dramatic increase compared to 31%. Spending money on advertising is a wise choice.
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