document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=488990>Question 488990</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If I drop three coins on a table, what is the probability of finding<BR>\n" );
document.write( "   1. exactly 2 heads<BR>\n" );
document.write( "   2. at most 1 head<BR>\n" );
document.write( "   3. at least 2 heads<BR>\n" );
document.write( "   4. at least 1 head<BR>\n" );
document.write( "sample space = 8\r<BR>\n" );
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document.write( "I came up with HHT, HTH, THH,HTT,THT,TTH,TTT,HHH.<BR>\n" );
document.write( "state the probability of each in the form of fraction and percent.<BR>\n" );
document.write( "For 1,2,3 I came up with 1/4 or .25, and for 4 = 1/6.<BR>\n" );
document.write( "Have I done this correctly, or can you show me a better way to show this??<BR>\n" );
document.write( "Is this a form of \"classical probability\"??<BR>\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333500 by </B><A HREF=/tutors/aboutme.mpl?userid=chessace><B>chessace(471)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chessace><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=chessace><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Good that you tried.<BR>\n" );
document.write( "For something this small, it's fine just to list all possibilities, but this should be done systematically to avoid missing or double counting.<BR>\n" );
document.write( "I.e., HHH HHT HTH HTT THH THT TTH TTT (count H=0 and T=1 and this is counting in binary from 0 to 7).<BR>\n" );
document.write( "Possibly because your list was random, you \"didn't count perfectly\".<BR>\n" );
document.write( "1. Has 3 hits, P = 3/8<BR>\n" );
document.write( "2. Has 4 hits, P = 1/2<BR>\n" );
document.write( "3. Is exactly like 2 because H and T are symetric. P = 1/2<BR>\n" );
document.write( "4. It is impossible to get any probability out of this example = 1/6; P = 7/8.\r<BR>\n" );
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document.write( "There is indeed a better way to do this.<BR>\n" );
document.write( "Note that none of the 4 questions care about the order, which is reasonable since the coins were dropped all at once.<BR>\n" );
document.write( "Thus you can expand (H+T)^3 [works for any \"3\", e.g., 5 coins --> (H+T)^5]<BR>\n" );
document.write( "HHH + 3HHT + 3HTT + TTT  (not in any coin order, just H written before T).<BR>\n" );
document.write( "Meaning: There is only one way to get all H; 3 ways to get HHT = 3 ways to pick which coin is the T.<BR>\n" );
document.write( "From this you just look [and add]:<BR>\n" );
document.write( "1. 2nd term: 3 --> 3/8<BR>\n" );
document.write( "2. 3rd and 4th terms: 3+1 = 4 --> 1/2<BR>\n" );
document.write( "3. 1st and 2nd terms: 4<BR>\n" );
document.write( "4. 1st 3 terms: 1+3+3 = 7<BR>\n" );
document.write( "Yes, this is \"classic probability\" although I haven't heard that term.<BR>\n" );
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