document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138983>Question 1138983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a particular math class, an instructor is giving a 15 question \"true or false\" quiz and the sequence of correct and incorrect answer is observed. A monkey strolls into the class grabs a quiz from the instructor, sits down and randomly selects either true or false for each of the questions, hands the completed quiz to the bewildered instructor, and walks out the classroom. Calculate the probabilities, should have four decimal place accuracy. <BR>\n" );
document.write( "a.) What is the probability that the monkey will get less than 75% on the quiz? <BR>\n" );
document.write( "b.) Which situation (situation 1 or 2) has the higher probability of occurring, situation 1: the monkey either gets 3,6, or 8 correct answers or situation 2: the monkey either gets 5,6, or 9 correct answers.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756804 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <b>a.) What is the probability that the monkey will get less than 75% on the quiz?</b><BR>\n" );
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document.write( "75% of 15 correct answers is 11.25 answers.  Therefore, we are being asked what the probability is that the monkey gets 11 or fewer correct answers.  The easiest way to do this is to figure out the probability the monkey gets 12 or more correct answers, then subtract this result from 1.<BR>\n" );
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document.write( "Probability of exactly 15 correct answers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5%5E15 ALIGN=MIDDLE  ALT=\"0.5%5E15\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.00003<BR>\n" );
document.write( "Probability of exactly 14 correct answers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%5E14%29%2A%280.5%5E1%29%2A%2815%21%2F%2814%21%2A1%21%29%29 ALIGN=MIDDLE  ALT=\"%280.5%5E14%29%2A%280.5%5E1%29%2A%2815%21%2F%2814%21%2A1%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.00046<BR>\n" );
document.write( "Probability of exactly 13 correct answers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%5E13%29%2A%280.5%5E2%29%2A%2815%21%2F%2813%21%2A2%21%29%29 ALIGN=MIDDLE  ALT=\"%280.5%5E13%29%2A%280.5%5E2%29%2A%2815%21%2F%2813%21%2A2%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.00320<BR>\n" );
document.write( "Probability of exactly 12 correct answers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%5E12%29%2A%280.5%5E3%29%2A%2815%21%2F%2812%21%2A3%21%29%29 ALIGN=MIDDLE  ALT=\"%280.5%5E12%29%2A%280.5%5E3%29%2A%2815%21%2F%2812%21%2A3%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.01389<BR>\n" );
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document.write( "Probability of 12 or more correct answers: 0.00003 + 0.00046 + 0.00320 + 0.01389 = 0.01758<BR>\n" );
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document.write( "Probability of 11 or fewer correct answers: 1 - 0.01758 = 0.98242. (Rounded off to four decimals, the answer is 0.9824.)<BR>\n" );
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document.write( "<b>b.) Which situation (situation 1 or 2) has the higher probability of occurring, situation 1: the monkey either gets 3,6, or 8 correct answers or situation 2: the monkey either gets 5,6, or 9 correct answers.</b><BR>\n" );
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document.write( "Situation 1:<BR>\n" );
document.write( "Probability of exactly 3 correct answers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%5E3%29%2A%280.5%5E12%29%2A%2815%21%2F%283%21%2A12%21%29%29 ALIGN=MIDDLE  ALT=\"%280.5%5E3%29%2A%280.5%5E12%29%2A%2815%21%2F%283%21%2A12%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.01389<BR>\n" );
document.write( "Probability of exactly 6 correct answers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%5E6%29%2A%280.5%5E9%29%2A%2815%21%2F%286%21%2A9%21%29%29 ALIGN=MIDDLE  ALT=\"%280.5%5E6%29%2A%280.5%5E9%29%2A%2815%21%2F%286%21%2A9%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.15274<BR>\n" );
document.write( "Probability of exactly 8 correct answers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%5E8%29%2A%280.5%5E7%29%2A%2815%21%2F%288%21%2A7%21%29%29 ALIGN=MIDDLE  ALT=\"%280.5%5E8%29%2A%280.5%5E7%29%2A%2815%21%2F%288%21%2A7%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.19638<BR>\n" );
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document.write( "Probability of either 3, 6, or 8 correct answers: 0.01389 + 0.15274 + 0.19638 = 0.36301<BR>\n" );
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document.write( "Situation 2:<BR>\n" );
document.write( "Probability of exactly 5 correct answers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%5E5%29%2A%280.5%5E10%29%2A%2815%21%2F%285%21%2A10%21%29%29 ALIGN=MIDDLE  ALT=\"%280.5%5E5%29%2A%280.5%5E10%29%2A%2815%21%2F%285%21%2A10%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.09164<BR>\n" );
document.write( "Probability of exactly 6 correct answers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%5E6%29%2A%280.5%5E9%29%2A%2815%21%2F%286%21%2A9%21%29%29 ALIGN=MIDDLE  ALT=\"%280.5%5E6%29%2A%280.5%5E9%29%2A%2815%21%2F%286%21%2A9%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.15274<BR>\n" );
document.write( "Probability of exactly 9 correct answers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%5E9%29%2A%280.5%5E6%29%2A%2815%21%2F%289%21%2A6%21%29%29 ALIGN=MIDDLE  ALT=\"%280.5%5E9%29%2A%280.5%5E6%29%2A%2815%21%2F%289%21%2A6%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.15274<BR>\n" );
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document.write( "Probability of either 5, 6, or 9 correct answers: 0.09164 + 0.15274 + 0.15274 = 0.39712<BR>\n" );
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document.write( "Situation 2 has the higher probability of occurring. </SPAN>\n" );
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