document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162805>Question 1162805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Gillian and Jonathan are playing a coin tossing game. Each one starts with 3 looneys. At each turn,<BR>\n" );
document.write( "one of the players takes one of his looneys and tosses it. If it comes up heads, the tosser loses, and<BR>\n" );
document.write( "must give the looney to the other player. If it comes up tails, the tosser wins, and gets to keeps the<BR>\n" );
document.write( "looney. In either case the loser has to toss his or her looney on the next turn. If one person loses all<BR>\n" );
document.write( "their looneys, the game is over.<BR>\n" );
document.write( "(a) Suppose that Gillian and Jonathan decide that if the game is not over by the fifth turn, they will<BR>\n" );
document.write( "stop anyway. Let Jonathan have the first toss.<BR>\n" );
document.write( "i. Write out all the elementary events in the sample space for this experiment. Would they be<BR>\n" );
document.write( "equally likely?<BR>\n" );
document.write( "ii. Let Fi be the event that the game is over after i turns (i = 1, . . . , 5). Find the probability of<BR>\n" );
document.write( "each Fi<BR>\n" );
document.write( ". Should these probabilities sum to 1?<BR>\n" );
document.write( "iii. Let Ei be the event that each player still has three looneys after the i<BR>\n" );
document.write( "th turn. Find the<BR>\n" );
document.write( "probability of each Ei<BR>\n" );
document.write( ". Should these probabilities sum to 1?<BR>\n" );
document.write( "iv. Find the probability that Gillian loses all her looneys.<BR>\n" );
document.write( "(b) Suppose that Gillian and Jonathan had not decided to end the game after five turns. Is it possible<BR>\n" );
document.write( "for the game to go on forever? What would be the probability that the game never stops? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786688 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=786688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "In my life, I saw tens of thousands of Math problems, and solved thousands of them,\r<BR>\n" );
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document.write( "and I firmly believe that there is no Math problem longer than 5 lines of standard format.\r<BR>\n" );
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document.write( "All the rest is EITHER essays OR nonsense.\r<BR>\n" );
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document.write( "More concretely, it is not clear to me, for what purpose/purposes this post was submitted to the forum ?\r<BR>\n" );
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document.write( "If a person wants to learn on solving Probability problems, he (or she) should start from basic problems,\r<BR>\n" );
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document.write( "which all and always are short in their formulation.\r<BR>\n" );
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document.write( "Also, the laws of the nature are such that nobody will not only solve, but even read so long text\r<BR>\n" );
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document.write( "without a vital necessity, excepting it is of extraordinary interest, which is definitely not the case.\r<BR>\n" );
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document.write( "If a visitor does expect that the tutors will work instead of him (or her), then the visitor makes a HUGE mistake.\r<BR>\n" );
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document.write( "Our goal at this forum is not to work instead of students, making their job, but to TEACH them.\r<BR>\n" );
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document.write( "Assuming that the students are able to learn and really want to do it . . . \r<BR>\n" );
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document.write( " </SPAN>\n" );
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