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" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823912 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a ball is returned, this is like two 10-side dice being rolled.<BR>\n" );
document.write( "There are 100 different outcomes from 1/1 to 10/10<BR>\n" );
document.write( "The smallest sum is 2, the largest 20, each of those two values with 1/100 probability <BR>\n" );
document.write( "3 will have 2/100 probability (1/2 an 2/1)<BR>\n" );
document.write( "4 will have 3/100...<BR>\n" );
document.write( "from the other side<BR>\n" );
document.write( "20 will have 1/100 probability<BR>\n" );
document.write( "19 will have 2/100 (9/10. 10/9)<BR>\n" );
document.write( "18 will have 3/100 (8/10, 10/8, 9/9)<BR>\n" );
document.write( "17 will have 4/100<BR>\n" );
document.write( "16 will have 5/100<BR>\n" );
document.write( "15 will have 6/100 probability (7/8,8/7,6/9,9/6,5/10,10/5).<BR>\n" );
document.write( "The answer is 21/100.<BR>\n" );
document.write( "the most probable outcome is a sum of 11 with 6 and 5; 7 and 4; 8 and 3; 9 and 2; 10 and 1, each twice or 1/10 probability. Contrast this with two cubic die with a maximum sum of 12, the most probable one of 7 (1 more than the number of sides), with a probability of 1/6 (as if one die were rolled).<BR>\n" );
document.write( "-<BR>\n" );
document.write( "if the ball has an even number, there are 5 possibilities, 2,4,6,8,10<BR>\n" );
document.write( "Two of these possibilities can be excluded immediately, 2 and 4, since ball 2 won't make a difference.<BR>\n" );
document.write( "if it is a 10, with probability 1/10, 6 of the 10 possibilities of ball 2 will work, so that probability is (1/10)(3/5)=3/50.<BR>\n" );
document.write( "If it is an 8, 4 of 10 possibilities will work, so that probability is (1/10)(2/5)=2/50.<BR>\n" );
document.write( "If it is a 6, 2 of 10 possibilities will work, so that probability is (1/10)(1/5)=1/50.<BR>\n" );
document.write( "The answer is the sum of those 3 or 6/50 or 12%. </SPAN>\n" );
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