document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976927>Question 976927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:<BR>\n" );
document.write( " = chocolate chosen <BR>\n" );
document.write( " = strawberry chosen<BR>\n" );
document.write( " = vanilla chosen<BR>\n" );
document.write( " = ice cream on a cone<BR>\n" );
document.write( " ice cream in a cup\r<BR>\n" );
document.write( "\n" );
document.write( "Find the probability that the ice cream was strawberry flavor, given that it was sold on a cone </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598625 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=598625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's think of what happens for every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000 ALIGN=MIDDLE  ALT=\"10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > servings of ice cream sold.<BR>\n" );
document.write( "For every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000 ALIGN=MIDDLE  ALT=\"10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > servings of ice cream sold,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2245%25%22 ALIGN=MIDDLE  ALT=\"%2245%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.45%2A10000=4500 ALIGN=MIDDLE  ALT=\"0.45%2A10000=4500\"   DISABLED_style= \"max-width:90%; height:auto;\" > are chocolate,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2230%25%22 ALIGN=MIDDLE  ALT=\"%2230%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.30%2A10000=3000 ALIGN=MIDDLE  ALT=\"0.30%2A10000=3000\"   DISABLED_style= \"max-width:90%; height:auto;\" > are strawberry,<BR>\n" );
document.write( "and the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22100%25%22-%2245%25%22-%2230%25%22=%2225%25%22 ALIGN=MIDDLE  ALT=\"%22100%25%22-%2245%25%22-%2230%25%22=%2225%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000-4500-3000=2500 ALIGN=MIDDLE  ALT=\"10000-4500-3000=2500\"   DISABLED_style= \"max-width:90%; height:auto;\" > are vanilla.<BR>\n" );
document.write( "Of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4500 ALIGN=MIDDLE  ALT=\"4500\"   DISABLED_style= \"max-width:90%; height:auto;\" > servings of chocolate ice cream sold,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2275%25%22 ALIGN=MIDDLE  ALT=\"%2275%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.75%2A4500=3375 ALIGN=MIDDLE  ALT=\"0.75%2A4500=3375\"   DISABLED_style= \"max-width:90%; height:auto;\" > were served in cones,<BR>\n" );
document.write( "while the other <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4500-3375=1125 ALIGN=MIDDLE  ALT=\"4500-3375=1125\"   DISABLED_style= \"max-width:90%; height:auto;\" > were served in cups.<BR>\n" );
document.write( "Of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000 ALIGN=MIDDLE  ALT=\"3000\"   DISABLED_style= \"max-width:90%; height:auto;\" > servings of strawberry ice cream sold,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2260%25%22 ALIGN=MIDDLE  ALT=\"%2260%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.60%2A3000=1800 ALIGN=MIDDLE  ALT=\"0.60%2A3000=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > were served in cones,<BR>\n" );
document.write( "while the other <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000-1800=1200 ALIGN=MIDDLE  ALT=\"3000-1800=1200\"   DISABLED_style= \"max-width:90%; height:auto;\" > were served in cups.<BR>\n" );
document.write( "Of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500 ALIGN=MIDDLE  ALT=\"2500\"   DISABLED_style= \"max-width:90%; height:auto;\" > servings of vanilla ice cream sold,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2240%25%22 ALIGN=MIDDLE  ALT=\"%2240%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.40%2A2500=1000 ALIGN=MIDDLE  ALT=\"0.40%2A2500=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > were served in cones,<BR>\n" );
document.write( "while the other <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500-1000=1500 ALIGN=MIDDLE  ALT=\"2500-1000=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" > were served in cups.<BR>\n" );
document.write( " <BR>\n" );
document.write( "We knew, without calculations that<BR>\n" );
document.write( "the probability of a serving being chocolate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2245%25%22=0.45 ALIGN=MIDDLE  ALT=\"%2245%25%22=0.45\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the probability of a serving being strawberry is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2230%25%22=0.30 ALIGN=MIDDLE  ALT=\"%2230%25%22=0.30\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <BR>\n" );
document.write( "the probability of a serving being vanilla is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2225%25%22=0.25 ALIGN=MIDDLE  ALT=\"%2225%25%22=0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since out of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000 ALIGN=MIDDLE  ALT=\"10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > servings, there were<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3375 ALIGN=MIDDLE  ALT=\"3375\"   DISABLED_style= \"max-width:90%; height:auto;\" > chocolate ice cream cones,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1800 ALIGN=MIDDLE  ALT=\"1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > strawberry ice cream cones, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" > vanilla ice cream cones,<BR>\n" );
document.write( "the total number of cones served was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3375%2B1800%2B1000=6175 ALIGN=MIDDLE  ALT=\"3375%2B1800%2B1000=6175\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, the probability of a serving being a cone is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6175%2F1000=.6175=%2261.75%25%22 ALIGN=MIDDLE  ALT=\"6175%2F1000=.6175=%2261.75%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Of course, that makes the probability of a serving being ice cream in a cup<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22100%25%22-%2261.75%25%22=%2238.25%25%22=0.3825 ALIGN=MIDDLE  ALT=\"%22100%25%22-%2261.75%25%22=%2238.25%25%22=0.3825\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6175 ALIGN=MIDDLE  ALT=\"6175\"   DISABLED_style= \"max-width:90%; height:auto;\" > cones served,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1800 ALIGN=MIDDLE  ALT=\"1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > were strawberry ice cream cones,<BR>\n" );
document.write( "the probability that the ice cream was strawberry flavor, given that it was sold on a cone is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1800%2F6175=about0.2915=%2229.15%25%22 ALIGN=MIDDLE  ALT=\"1800%2F6175=about0.2915=%2229.15%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( ", , and 40%, </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );