document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214953>Question 214953</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five counters are selected at random from an urn which contains ten white<BR>\n" );
document.write( "and forty black counters. Find the probability that exactly two of the se-<BR>\n" );
document.write( "lected counters are white if the selections are made: (i) without replace-<BR>\n" );
document.write( "ment; (ii) with replacement.<BR>\n" );
document.write( "In case (i) fnd the probability that at least two of the selected counters<BR>\n" );
document.write( "are white. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162431 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=162431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Five counte/rs are selected at random from an urn which contains ten white<BR>\n" );
document.write( "and forty black counters. <BR>\n" );
document.write( "Find the probability that exactly two of the selected counters are white <BR>\n" );
document.write( "if the selections are made: <BR>\n" );
document.write( "(i) without replacement<BR>\n" );
document.write( "P(2 white without replacement) = (10/50)(9/49)(40/48)(39/47)(38/46) <BR>\n" );
document.write( "------------------------------------------------- <BR>\n" );
document.write( "(ii) with replacement <BR>\n" );
document.write( "P(2 white with replacement) = 5C2*(10/50)^2(40/50)^3 = 0.2048..<BR>\n" );
document.write( "--------------------------------------------------<BR>\n" );
document.write( "In case (i) fnd the probability that at least two of the selected counters<BR>\n" );
document.write( "are white.<BR>\n" );
document.write( "P(at least two white without replacement)<BR>\n" );
document.write( "= 1 - [P(none white) + P(1 white)]<BR>\n" );
document.write( "------<BR>\n" );
document.write( "P(none white) = 40C5/50C5 <BR>\n" );
document.write( "P(one white) = (10/50)(40/49)(39/48)(38/47)(37/46)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "I'll leave the arithmetic to you.<BR>\n" );
document.write( "========================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );