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 #391976 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=391976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5 question test.<BR>\n" );
document.write( "true or false answer on each question.<BR>\n" );
document.write( "student randomly guesses each answer.<BR>\n" );
document.write( "probability of getting the question right is 50%<BR>\n" );
document.write( "probability of getting the question wrong is 50%\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( "probability he gets the first question right is 1/2.\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( "probability he gets the first 3 questions right is 1/2 * 1/2 * 1/2 = 1/8\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( "probability he gets at least one question right is equal to 1 minus the probability he gets no questions right.\r<BR>\n" );
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document.write( "probability he gets no questions right is 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 which is equal to 1/2^5 whgich is equal to 1/32.\r<BR>\n" );
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document.write( "probability he gets at least 1 question right is 1 minus 1/32 which is equal to 31/32.\r<BR>\n" );
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document.write( "since this is a 5 question test, n would be equal to 5, not 10.\r<BR>\n" );
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document.write( "that last question deals with the binomial distribution probabilities.\r<BR>\n" );
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document.write( "here's how it works.\r<BR>\n" );
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document.write( "p is equal to the probability of getting it right which is equal to .5<BR>\n" );
document.write( "q is equal to the probability of getting it wrong which is equal to 1 - .5 which is equal to .5<BR>\n" );
document.write( "just so happens those probabilities are the same but don't have to be.<BR>\n" );
document.write( "n is equal to 5.<BR>\n" );
document.write( "C(n,x) is the combination formula which is equal to n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "binomial distribution for this problem would be:\r<BR>\n" );
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document.write( "p(0 right) = C(5,0) * .5^0 * .5^5 = 1 * 1 * .03125 = .03125<BR>\n" );
document.write( "P(1 right) = C(5,1) * .5^1 * .5^4 = 5 * .5 * .0625 = .15625<BR>\n" );
document.write( "p(2 right) = C(5,2) * .5^2 * .5^3 = 10 * .25 * .125 = .3125<BR>\n" );
document.write( "p(3 right) = C(5,3) * .5^3 * .5^2 = 10 * .125 * .25 = .3125<BR>\n" );
document.write( "p(4 right) = C(5,4) * .5^4 * .5^1 = 5 * .0625 * .5 = .15625<BR>\n" );
document.write( "p(5 right) = C(5,5) * .5^5 * .5^0 = 1 * .03125 * 1 = .03125\r<BR>\n" );
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document.write( "add up all the probabilities and they should be equal to 1.<BR>\n" );
document.write( "they are.<BR>\n" );
document.write( "probability of getting at least 1 right is equal to 1 minus .03125 which is equal to .96875 which is equal to 31/32.<BR>\n" );
document.write( "probability of getting at least 1 right is equal to p(1) + p(2) + p(3) + p(4) + p(5) which is equal to the same things.\r<BR>\n" );
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document.write( "part a is only asking you for the probability of getting the first one right and doesn't consider whether the others are right or wrong so you deal with that separately.\r<BR>\n" );
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document.write( "part b is only asking you for the probability of getting the first 3 right and doesn' consider whether the others are right or wrong so you deal with that separately.\r<BR>\n" );
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document.write( "the last questions deals with the binomial distribution and you use the formula for that.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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