document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475963>Question 475963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm wondering, what is least likely to happen:<BR>\n" );
document.write( "to pick (randomly from a deck of 52)<BR>\n" );
document.write( "all 7's in a deck of cards without replacement and no shuffling<BR>\n" );
document.write( "all 7's in a deck without replacement but with shuffling<BR>\n" );
document.write( "all 7's in a deck with replacement and with shuffling<BR>\n" );
document.write( "or<BR>\n" );
document.write( "to pick all 7's in a deck with replacement and without shuffling? <BR>\n" );
document.write( "Which one is the least probable and what is the probability of such an event occurring? Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326419 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=326419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm wondering, what is least likely to happen:<BR>\n" );
document.write( "to pick (randomly from a deck of 52)<BR>\n" );
document.write( "all 7's in a deck of cards without replacement and no shuffling<BR>\n" );
document.write( "all 7's in a deck without replacement but with shuffling<BR>\n" );
document.write( "all 7's in a deck with replacement and with shuffling<BR>\n" );
document.write( "or<BR>\n" );
document.write( "to pick all 7's in a deck with replacement and without shuffling? <BR>\n" );
document.write( "----<BR>\n" );
document.write( "The shuffling has no effect as long as the selections are<BR>\n" );
document.write( "made randomly.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Replacement does have an effect:<BR>\n" );
document.write( "with replacement: (1/13)^4 = 1/28561<BR>\n" );
document.write( "---<BR>\n" );
document.write( "without replacement: 1/52C4 = 1/270725<BR>\n" );
document.write( "===========<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );