document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202960>Question 1202960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number is chosen at random from 1 to 600 inclusive. What is the probability that it will have at least 2 digits equal to 5? </SPAN>\n" );
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document.write( "Answer:  <font color=red size=4>1/25</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Let x be a number from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}\r<BR>\n" );
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document.write( "In the case of 55x, there are 10 values possible<BR>\n" );
document.write( "550, 551, 552, 553, 554, 555, 556, 557, 558, 559\r<BR>\n" );
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document.write( "The same goes for the 5x5 case<BR>\n" );
document.write( "505, 515, 525, 535, 545, 555, 565, 575, 585, 595<BR>\n" );
document.write( "However notice how 555 has been repeated.<BR>\n" );
document.write( "This means we have really introduced 9 extra cases (not 10) to have 10+9 = 19 cases so far.\r<BR>\n" );
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document.write( "Then for the x55 case we have 6 more values, but we'll exclude 555 of course.<BR>\n" );
document.write( "55, 155, 255, 355, 455, 555<BR>\n" );
document.write( "So we're adding 5 more cases to get 19+5 = 24 cases total\r<BR>\n" );
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document.write( "Here are all 24 items arranged in a 6 row 4 column table<BR>\n" );
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document.write( "<tr><TD >55</TD><TD >155</TD><TD >255</TD><TD >355</TD></tr><tr><TD >455</TD><TD >505</TD><TD >515</TD><TD >525</TD></tr><tr><TD >535</TD><TD >545</TD><TD >550</TD><TD >551</TD></tr><tr><TD >552</TD><TD >553</TD><TD >554</TD><TD >555</TD></tr><tr><TD >556</TD><TD >557</TD><TD >558</TD><TD >559</TD></tr><tr><TD >565</TD><TD >575</TD><TD >585</TD><TD >595</TD></tr>\n" );
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document.write( "There are 24 values that have at least two digits of 5, out of 600 values total.\r<BR>\n" );
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document.write( "24/600 = (1*24)/(25*24) = <font color=red size=4>1/25</font> is the fractional probability of getting such a value. \r<BR>\n" );
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document.write( "1/25 = 0.04 in decimal form.<BR>\n" );
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