document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=623118>Question 623118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> .  A student is taking a 5 question True-False quiz but he has not been doing any work in the course and does not know the material so he randomly guesses at all the answers. \r<BR>\n" );
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document.write( "a) What is the probability that he gets the first question right?\r<BR>\n" );
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document.write( "b) What is the probability that he gets the first three questions right?\r<BR>\n" );
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document.write( "c) What is the probability that he gets at least one question right?\r<BR>\n" );
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document.write( "First of all, I don't understand the difference between Question a and Question c. Also, I read some other examples but I do not get yet on this website and my book, and still can not answer these questions. <BR>\n" );
document.write( "So far I have done this\r<BR>\n" );
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document.write( "P= .5 since they are true and false.<BR>\n" );
document.write( "n= 10 since they are 10 question <BR>\n" );
document.write( " But I dont know how to use this data. help please!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391978 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=391978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) As you already figured out, the probability of randomly guessing a true/false question is 0.5 or 1/2<br><BR>\n" );
document.write( "b) The probability of getting all of the first three questions right  is the product of the probabilities of getting each one right:<BR>\n" );
document.write( "0.5*0.5*0.5 = 0.125 or 1/8<br><BR>\n" );
document.write( "c) Are there 5 questions or 10? At the beginning you say there are 5 but then later you say there are 10. Since I do not know which, I will just tell you how to find the answer.<br><BR>\n" );
document.write( "These problems where you are to \"find the probability of at least 1 ...\" can be done by finding the probability of exactly 1 right, the probability of exactly 2 right, etc. and then adding all of them together to find the probability of at least one. It can be done this way but those probabilities are not easy to figure out and you would n of those probabilities to calculate.<br><BR>\n" );
document.write( "Fortunately there is a much easier way. It takes advantage of the fact that all the probabilities of all the possible events always add up to 1. The only event, other than getting at least one right, is that he gets none right. (Think about it.) So:<BR>\n" );
document.write( "P(at least one right) + P(none right) = 1<BR>\n" );
document.write( "or<BR>\n" );
document.write( "P(at least one right) = 1 - P(none right)<BR>\n" );
document.write( "It is much easier to find just the one probability and then subtract it from 1.<br><BR>\n" );
document.write( "So we will find the probability of getting none right. On a true/false test the probability of getting a question wrong is the same as the probability of getting it right: 0.5. The probability of getting all n questions wrong would be the product of n 0.5's, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%29%5En ALIGN=MIDDLE  ALT=\"%280.5%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This makes the probability of getting at least one right:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+%280.5%29%5En ALIGN=MIDDLE  ALT=\"1+-+%280.5%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now just use your calculator and the correct value for n to figure out the answer. </SPAN>\n" );
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