document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=373745>Question 373745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.\r<BR>\n" );
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document.write( "Thanks!\r<BR>\n" );
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document.write( "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.   \r<BR>\n" );
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document.write( " 	Number of Products Purchased	 <BR>\n" );
document.write( "Brands Purchased	Fewer	Same	More	Total<BR>\n" );
document.write( "Same......................10......14......24.......48<BR>\n" );
document.write( "Changed...............262.....82......8........352<BR>\n" );
document.write( "Total.....................272.....96......32.......400\r<BR>\n" );
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document.write( "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.  ________   \r<BR>\n" );
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document.write( "  **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.**\r<BR>\n" );
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document.write( "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.  ________	\r<BR>\n" );
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document.write( "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.  ________\r<BR>\n" );
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document.write( "            ** 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??**\r<BR>\n" );
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document.write( "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.  ________<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266123 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) There are 272 people who purchased fewer products out of a total of 400 <BR>\n" );
document.write( "people. So the probability is 272/400 = 0.68, which means you have the <BR>\n" );
document.write( "correct answer. If you want to be really technical, you can write 0.68 as <BR>\n" );
document.write( "0.6800 (which is to 4 decimal places), but it's not necessary.\r<BR>\n" );
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document.write( "B)\r<BR>\n" );
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document.write( "There are 96 people total who purchased the same amount and 32 total who <BR>\n" );
document.write( "purchased more. Add these up to get 96+32 = 128\r<BR>\n" );
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document.write( "So 128 people purchased the same or more. This is out of 400 total.\r<BR>\n" );
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document.write( "So the probability is 128/400 = 8/25 = 0.32\r<BR>\n" );
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document.write( "Note: this is possible since the events are mutually exclusive.\r<BR>\n" );
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document.write( "C) \r<BR>\n" );
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document.write( "Assuming that the two events are independent, you're simply multiplying <BR>\n" );
document.write( "the two probabilities of purchasing fewer brands and changing brands.\r<BR>\n" );
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document.write( "So the answer is (272/400)*(352/400) = 374/625 = 0.5984\r<BR>\n" );
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document.write( "If the two events are not independent, then...\r<BR>\n" );
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document.write( "P(Purchased fewer than before AND changed brands) = P(Purchased fewer than before)*P(changed brands given that purchased fewer than before)<BR>\n" );
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document.write( "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 ) <BR>\n" );
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document.write( "So this means that<BR>\n" );
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document.write( "P(Purchased fewer than before AND changed brands) = (272/400)*(262/272)<BR>\n" );
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document.write( "which becomes<BR>\n" );
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document.write( "P(Purchased fewer than before AND changed brands) = 262/400 <BR>\n" );
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document.write( "and reduces to <BR>\n" );
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document.write( "P(Purchased fewer than before AND changed brands) = 131/200 <BR>\n" );
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document.write( "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)<BR>\n" );
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document.write( "So the idea is very similar if the two events were independent, but we have that conditional probability to worry about now.\r<BR>\n" );
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document.write( "D) \r<BR>\n" );
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document.write( "Since it's \"Given that a consumer changed the brands\", this means that we <BR>\n" );
document.write( "know for sure that the consumer changed brands and that we only need to <BR>\n" );
document.write( "focus on row 2. Everything else is irrelevant.\r<BR>\n" );
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document.write( "So in row 2, we see that 262 people purchased fewer products and this is out <BR>\n" );
document.write( "of 352 people who changed total.\r<BR>\n" );
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document.write( "So the probability is 262/352 = 131/176 = 0.744318\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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