document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043824>Question 1043824</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mario and Bowser begin with a hat that has 5 balls in it: 3 are red, 2 are green. Bowser secretly picks a ball and tells Mario it is red, although he might be lying about the color. If there is an 80% chance Bowser is lying, what is the probability that Mario draws 2 red balls in a row after Bowser's initial draw?<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 #659193 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> hat has 5 balls in it.<BR>\n" );
document.write( "3 are red and 2 are green.<BR>\n" );
document.write( "bowser takes a ball out and says it's red.\r<BR>\n" );
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document.write( "80% chance bowser is lying.<BR>\n" );
document.write( "20% chance bowser is telling the truth.\r<BR>\n" );
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document.write( "what is the probbility that mario will get 2 balls out of the hat that are both red?\r<BR>\n" );
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document.write( "probabilities and percentages are linked together in that, if something occurs 80% of the time, then the probability that it will occur the next time is 80%.\r<BR>\n" );
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document.write( "the inherent assumption is that, if the probability is 80%, then if you repeat the experiment an infinite number of times, the frequency of occurrence will be 80% as well.\r<BR>\n" );
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document.write( "flip a coin is an example.<BR>\n" );
document.write( "the probability of getting heads in a fair coin is 50%.<BR>\n" );
document.write( "if you flip the coin an infinite number of times, heads will come up 50% of the time.\r<BR>\n" );
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document.write( "same type of thing happens with this.\r<BR>\n" );
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document.write( "80% of the time bowser is lying, so 80% of the time there will be 3 red balls and 1 green ball in the hat after he draws a ball out of it.<BR>\n" );
document.write( "the probability of getting 2 red balls in a row will be 3/4 * 2/3 = 6/12 = 1/2.\r<BR>\n" );
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document.write( "20% of the time bowser is telling the truth, so 20% of the time there will be 2 red balls and 2 green balls in the hat after he draws a ball out of it.<BR>\n" );
document.write( "the probability of getting 2 red balls in a row will be 2/4 * 1/3 = 2/12 = 1/6.\r<BR>\n" );
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document.write( "80% = 8/10 = 4/5<BR>\n" );
document.write( "20% = 2/10 = 1/5\r<BR>\n" );
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document.write( "the total probability is (4/5 * 1/2) + (1/5 * 1/6) = 4/10 + 1/30 = 12/30 + 1/30 = 13/30.\r<BR>\n" );
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