document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=289119>Question 289119</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two integers from 1 to 10 are randomly selected. the same number may be chosen twice. what is the probability that both numbers are less than 9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209485 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=209485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: there are 10 numbers to choose from total in the range from 1 to 10. \r<BR>\n" );
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document.write( "Since the only two numbers that are NOT less than 9 is 9 itself and 10, this means that there are 8 numbers that are less than 9 (since 10-2=8)\r<BR>\n" );
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document.write( "P(number is less than 9) means \"the probability that the number is less than 9\"\r<BR>\n" );
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document.write( "P(number is less than 9) = number of numbers that are less than 9 from 1 to 10/total number of numbers = 8/10 = 4/5\r<BR>\n" );
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document.write( "So the probability of choosing ONE number that is less than 9 is 4/5. However, we want to know what the probability of choosing two numbers. So we need to slightly change the probability to: \r<BR>\n" );
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document.write( "P(choosing two numbers less than 9) = P(choosing number less than 9 AND choosing number less than 9) = P(number is less than 9)*P(number is less than 9) = (4/5)*(4/5) = 16/25\r<BR>\n" );
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document.write( "So the probability is 16/25 which in decimal form is 0.64 or an 64% chance. </SPAN>\n" );
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