document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61249>Question 61249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A statistics student needs a grade of at least 70 to pass an examination.  The exam consists of 10 true/false questions.  If he guesses at each question, what is the probability he will pass? and if the test was changed to 10 multiple-choice questions having 5 possible answers to choose from and he is still guessing what is the probability he will pass? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42222 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=42222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I hope you're allowed to use a TI-83 or 84 for this, otherwise, it's kind of a pain!<BR>\n" );
document.write( "A statistics student needs a grade of at least 70 to pass an examination.  The exam consists of 10 true/false questions.  If he guesses at each question, what is the probability he will pass? and if the test was changed to 10 multiple-choice questions having 5 possible answers to choose from and he is still guessing what is the probability he will pass?<BR>\n" );
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document.write( "This is a binomial probability problem.<BR>\n" );
document.write( "n=10  (The number of questions)<BR>\n" );
document.write( "p=.5  (1/2 chance of getting a true-false question right)<BR>\n" );
document.write( "q=1-.5=.5 (1/2 chance of getting it wrong)<BR>\n" );
document.write( "x=7,8,9,10 (because he can pass with a 70,80,90, or 100)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The formula is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P%28x%29=%28n%21%2F%28%28n-x%29%21%2Ax%21%29%29%2Ap%5Ex%2Aq%5E%28n-x%29%29 ALIGN=MIDDLE  ALT=\"highlight%28P%28x%29=%28n%21%2F%28%28n-x%29%21%2Ax%21%29%29%2Ap%5Ex%2Aq%5E%28n-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P(x)=probability of x<BR>\n" );
document.write( "n=number of trials<BR>\n" );
document.write( "x=number of successes<BR>\n" );
document.write( "p=probabillty of success<BR>\n" );
document.write( "q=1-p=probabilty of failure<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Add all the probability of x=7,8,9,10 together and the students has a probability of .171875 of passing.  If you have a TI-83/84 <BR>\n" );
document.write( "1-binomialcdf(10,.5,6)=.171875<BR>\n" );
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document.write( "For the second one, everything is the same except:<BR>\n" );
document.write( "p=1/5=.2 and q=4/5=.8<BR>\n" );
document.write( "Add the probabilities of x=7,8,9,10 together and the student has a .0008643584 chance of passing.<BR>\n" );
document.write( "1-binomialcdf(10,.2,6)=8.643584E-4=.0008643584<BR>\n" );
document.write( ":<BR>\n" );
document.write( "If I were the student, I'd study.  Both probabilities are low, and the chance of passing a multiple choice test by guessing is almost 0!<BR>\n" );
document.write( "That should be enough to help you solve it.  If not, let me know.<BR>\n" );
document.write( "Happy Calculating!!!<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );