document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163206>Question 1163206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 888.One stick is three times as long as another. You break the longer stick at a random point. Now you have three sticks. What is the probability that they form a triangle? </SPAN>\n" );
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document.write( "Let the lengths of the two sticks be x and 3x.  Call the short stick stick A.<br><BR>\n" );
document.write( "The longer stick is broken into two sticks.  Call them the left stick and the right stick.<br><BR>\n" );
document.write( "If the length of the left stick is less than x, then the length of the right stick is greater than 2x, and the lengths of A and the left stick together will be less than the length of the right stick, and no triangle can be formed.<br><BR>\n" );
document.write( "If the length of the left stick is greater than 2x, then the length of the right stick is less than x, and the lengths of A and the right stick together will be less than the length of the left stick, and no triangle can be formed.<br><BR>\n" );
document.write( "So, in order to be able to form a triangle, the length of the left stick must be between x and 2x, a range of x.<br><BR>\n" );
document.write( "And since the length of the original second stick was 3x, the probability that the three sticks form a triangle is x/3x = 1/3.<br><BR>\n" );
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