Question 373745: Hello, I am having a really hard time with this. I have tried to complete several of the sections, but I think I am getting lost somewhere. If you can help it would be great. There are four sections to be answered. I will show my work on the one's I have attempted.
Thanks!
In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer questions 9 through 12.
Number of Products Purchased
Brands Purchased Fewer Same More Total
Same......................10......14......24.......48
Changed...............262.....82......8........352
Total.....................272.....96......32.......400
A) What is the probability that a consumer selected at random purchased fewer products than before? Place your answer, rounded to 4 decimal places, in the blank. ________
**for this one I figured that I was looking at 272 which purchased fewer products, out of the 400 total purchased. So I had 272/400 = 0.68? But this is not four decimal places, so I figure I set something up wrong.**
B. What is the probability that a consumer selected at random purchased the same number or more products than before? Place your answer, rounded to 4 decimal places, in the blank. ________
C. What is the probability that a consumer selected at random purchased fewer products than before and changed brands? Place your answer, rounded to 4 decimal places, in the blank. ________
** for this I did the total purchased fewer as 262/400 and then changed as 352/400. I have the equation as P=262/400 % 352/400. This would then become P=262/400 *400/352 which would reduce down to 262/352 = 0.744318??**
D. Given that a consumer changed the brands, what then is the probability that the consumer purchased fewer products than before? Place your answer, rounded to 4 decimal places, in the blank. ________
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! A) There are 272 people who purchased fewer products out of a total of 400
people. So the probability is 272/400 = 0.68, which means you have the
correct answer. If you want to be really technical, you can write 0.68 as
0.6800 (which is to 4 decimal places), but it's not necessary.
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B)
There are 96 people total who purchased the same amount and 32 total who
purchased more. Add these up to get 96+32 = 128
So 128 people purchased the same or more. This is out of 400 total.
So the probability is 128/400 = 8/25 = 0.32
Note: this is possible since the events are mutually exclusive.
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C)
Assuming that the two events are independent, you're simply multiplying
the two probabilities of purchasing fewer brands and changing brands.
So the answer is (272/400)*(352/400) = 374/625 = 0.5984
If the two events are not independent, then...
P(Purchased fewer than before AND changed brands) = P(Purchased fewer than before)*P(changed brands given that purchased fewer than before)
Note: I'm using the formula P(A and B) = P( A ) * P(B | A). This formula holds true regardless if A and B are independent or not. This is because if A and B were independent, then P(B | A) = P( B )
So this means that
P(Purchased fewer than before AND changed brands) = (272/400)*(262/272)
which becomes
P(Purchased fewer than before AND changed brands) = 262/400
and reduces to
P(Purchased fewer than before AND changed brands) = 131/200
So the probability that a consumer selected at random purchased fewer products than before and changed brands is 131/200 which in decimal form is 0.655 (so it's a 65.5% chance)
So the idea is very similar if the two events were independent, but we have that conditional probability to worry about now.
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D)
Since it's "Given that a consumer changed the brands", this means that we
know for sure that the consumer changed brands and that we only need to
focus on row 2. Everything else is irrelevant.
So in row 2, we see that 262 people purchased fewer products and this is out
of 352 people who changed total.
So the probability is 262/352 = 131/176 = 0.744318
If you need more help, email me at jim_thompson5910@hotmail.com
Also, feel free to check out my tutoring website
Jim
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