document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171510>Question 171510</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321331793/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I need someone to double check my answer.\r<BR>\n" );
document.write( "\n" );
document.write( "One card is slected at random from a ordinary set of 52 cards.  Find the probability of each of the following events:  a spade and a 5 are drawn\r<BR>\n" );
document.write( "\n" );
document.write( "4 fives = heart, diamond, clover and spade<BR>\n" );
document.write( "14 spades - 1(5 of spades) = 13 spades\r<BR>\n" );
document.write( "\n" );
document.write( "4/52 = 1/13\r<BR>\n" );
document.write( "\n" );
document.write( "13/13 = 1\r<BR>\n" );
document.write( "\n" );
document.write( "I came up with answer of 1% </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126676 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, the statement describing the experiment is ambiguous.  Are you drawing one card and it must be exactly the 5 of spades, or are you drawing two cards, one of which must be a 5 and the other must be a spade?  Furthermore,  you don't specify if, on a two card draw, whether you are replacing the first card before making the second draw.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case 1:  One card draw and success = 5 of spades. Trivial.  There is only one 5 of spades in the deck, so your probability is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F52 ALIGN=MIDDLE  ALT=\"1%2F52\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case 2:  Two card draw with replacement and success = one card will be a spade of any rank and the other will be a 5 of any suit.\r<BR>\n" );
document.write( "\n" );
document.write( "First of all, there are 13 spades out of 52 cards, so the probability of drawing any spade is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F52 ALIGN=MIDDLE  ALT=\"13%2F52\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Second, there are four 5s in the deck, so the probability of drawing a 5 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F52 ALIGN=MIDDLE  ALT=\"4%2F52\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And the total probability is the product <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F52%2A4%2F52=52%2F2704 ALIGN=MIDDLE  ALT=\"13%2F52%2A4%2F52=52%2F2704\"   DISABLED_style= \"max-width:90%; height:auto;\" >, approximately 0.019 or 1.9%\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case 3: Two card draw WITHOUT replacement and success is the same as Case 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You have to consider the possibility that the first card drawn is the 5 of spades. So:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case 3a: The probability of drawing a spade other than the 5 times the probability of drawing a 5 when the deck is one card smaller <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F52%2A4%2F51 ALIGN=MIDDLE  ALT=\"12%2F52%2A4%2F51\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plus\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case 3b: The probability of drawing the 5 of spades times the probability of drawing a 5 with a deck that is one card smaller AND has one less 5 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F52%2A3%2F51 ALIGN=MIDDLE  ALT=\"1%2F52%2A3%2F51\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Total probability <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F52%2A4%2F51%29%2B%281%2F52%2A3%2F51%29 ALIGN=MIDDLE  ALT=\"%2812%2F52%2A4%2F51%29%2B%281%2F52%2A3%2F51%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > roughly the same value as Case 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case 4:  You really meant to ask \"What is the probability, on a one card draw, that the card will be a spade OR a 5\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Again 13 spades and 4 fives one of which is a spade and already counted, so there are 3 other suited fives, making a total of 16 cards that represent a successful experiment, and your probability is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F52 ALIGN=MIDDLE  ALT=\"16%2F52\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (You could also look at it as 4 fives and 12 spades that aren't a five adding up to the same 16 successes out of 52 possibilities.)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );