document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163707>Question 1163707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A coin is tossed 3 times. define the events A and B as:<BR>\n" );
document.write( "A = {num heads > num tails}<BR>\n" );
document.write( "B = {1st toss is a head}\r<BR>\n" );
document.write( "\n" );
document.write( "Find P(A|B) </SPAN>\n" );
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document.write( "P(A|B) is the probability that the number of heads is greater than the number of tails, given that the first toss is a head.<br><BR>\n" );
document.write( "So we know the first toss was a head; we need to determine whether in the last two tosses there is at least one more head.<br><BR>\n" );
document.write( "In two tosses of a coin, the probability of getting two tails is (1/2)(1/2) = 1/4; so the probability of getting at least one more head in the last two tosses is 3/4.<br><BR>\n" );
document.write( "ANSWER: P(A|B) = 3/4.<br><BR>\n" );
document.write( "There are many other formal methods for working the problem.<br><BR>\n" );
document.write( "However, note that with the small number of tosses, the fastest path to the answer is to write out all 2*2*2 = 8 possible outcomes of the three tosses and compute P(A|B) from looking at them.<br><BR>\n" );
document.write( "HHH<BR>\n" );
document.write( "HHT<BR>\n" );
document.write( "HTH<BR>\n" );
document.write( "HTT<BR>\n" );
document.write( "TTT<BR>\n" );
document.write( "TTH<BR>\n" );
document.write( "THT<BR>\n" );
document.write( "THH<br><BR>\n" );
document.write( "Throw out the last four since the first toss was not a head; then observe that in 3 of the other four the number of heads is greater than the number of tails.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );