document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186400>Question 1186400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.\r<BR>\n" );
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document.write( " 	18  -  24	25  -  34	35  -  55	55 and over	Total<BR>\n" );
document.write( "Liked Crunchicles	1	6	5	6	18<BR>\n" );
document.write( "Disliked Crunchicles	4	5	5	8	22<BR>\n" );
document.write( "No Preference	38	5	9	108	160<BR>\n" );
document.write( "Total	43	16	19	122	200\r<BR>\n" );
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document.write( "One consumer from the survey is selected at random. Use reduced fractions for your responses to each of the following questions.\r<BR>\n" );
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document.write( "What is the probability that the consumer is 18  -  24 years of age, given that they dislike Crunchicles?\r<BR>\n" );
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document.write( "What is the probability that the selected consumer dislikes Crunchicles?\r<BR>\n" );
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document.write( "What is the probability that the selected consumer is 35  -  55 years old or likes Crunchicles?\r<BR>\n" );
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document.write( "If the selected consumer is 70 years old, what is the probability that they like Crunchicles?\r<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 #849445 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the probabilities based on the given table:\r<BR>\n" );
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document.write( "**1. Probability that the consumer is 18-24 years of age, given that they dislike Crunchicles:**\r<BR>\n" );
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document.write( "We are given that the consumer dislikes Crunchicles. So, we focus on the \"Disliked Crunchicles\" row. The probability that they are 18-24 years old is:\r<BR>\n" );
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document.write( "P(18-24 | Disliked Crunchicles) = (Number of 18-24 who disliked) / (Total who disliked)<BR>\n" );
document.write( "P(18-24 | Disliked Crunchicles) = 4 / 22<BR>\n" );
document.write( "P(18-24 | Disliked Crunchicles) = **2/11**\r<BR>\n" );
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document.write( "**2. Probability that the selected consumer dislikes Crunchicles:**\r<BR>\n" );
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document.write( "This is simply the number of people who disliked Crunchicles divided by the total number of people surveyed:\r<BR>\n" );
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document.write( "P(Disliked Crunchicles) = 22 / 200<BR>\n" );
document.write( "P(Disliked Crunchicles) = **11/100**\r<BR>\n" );
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document.write( "**3. Probability that the selected consumer is 35-55 years old or likes Crunchicles:**\r<BR>\n" );
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document.write( "We need to consider the \"35-55\" column and the \"Liked Crunchicles\" row. However, we need to avoid double-counting the people who are both 35-55 years old and liked Crunchicles.\r<BR>\n" );
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document.write( "P(35-55 or Liked) = P(35-55) + P(Liked) - P(35-55 and Liked)<BR>\n" );
document.write( "P(35-55 or Liked) = (19/200) + (18/200) - (5/200)<BR>\n" );
document.write( "P(35-55 or Liked) = 32/200<BR>\n" );
document.write( "P(35-55 or Liked) = **8/50 = 4/25**\r<BR>\n" );
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document.write( "**4. If the selected consumer is 70 years old, what is the probability that they like Crunchicles?**\r<BR>\n" );
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document.write( "Since the consumer is 70 years old, they fall in the \"55 and over\" category. We focus on that column.\r<BR>\n" );
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document.write( "P(Liked | 55 and over) = (Number of 55 and over who liked) / (Total 55 and over)<BR>\n" );
document.write( "P(Liked | 55 and over) = 6 / 122<BR>\n" );
document.write( "P(Liked | 55 and over) = **3/61** </SPAN>\n" );
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