document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192023>Question 1192023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I have this problem I can't really solve: In the box there are balls with 1, 2, ..., 10 numbers on them. Two balls are randomly pulled one after the other with a return. <BR>\n" );
document.write( "a) What is the probability that the sum of the numbers written on the balls will be greater than 14?<BR>\n" );
document.write( "b) Then when pulling out the first ball, we see it with the even number on it. What is the probability that the sum of the numbers written on the balls will be greater than 14? </SPAN>\n" );
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document.write( "The number of possible outcomes is 10*10 = 100.<br><BR>\n" );
document.write( "(a) P(sum greater than 14)<br><BR>\n" );
document.write( "Outcomes with sum greater than 14:<BR>\n" );
document.write( "1st ball 10: 2nd ball 5, 6, ..., 10 (6 possibilities)<BR>\n" );
document.write( "1st ball 9: 2nd ball 6 to 10 (5 possibilities)<BR>\n" );
document.write( "1st ball 8: 2nd ball 7 to 10 (4)<BR>\n" );
document.write( "1st ball 7: 2nd ball 8 to 10 (3)<BR>\n" );
document.write( "1st ball 6: 2nd ball 9 or 10 (2)<BR>\n" );
document.write( "1st ball 5P 2nd ball 10 (1)<br><BR>\n" );
document.write( "Total good outcomes: 6+5+4+3+2+1 = 21<br><BR>\n" );
document.write( "P(sum greater than 14) = 21/100<br><BR>\n" );
document.write( "(b) P(sum greater than 14, given that the first ball is even)<br><BR>\n" );
document.write( "Using the list above, now the good outcomes are only if the first ball is 10, 8, or 6.<br><BR>\n" );
document.write( "Number of good outcomes: 6+4+2=12<br><BR>\n" );
document.write( "P(sum greater than 14) = 12/100<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );