document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100269>Question 1100269</A>: <I><SPAN STYLE=\"word-break: break-all;\"> our labelled 2, 2, 3 and 5 are put in a hat, Three cards are drawn, one at a time, and the number showing is recorded, The eard is not replaced,<BR>\n" );
document.write( "  (a) Draw up the sample space using 2A and 2H distinguish between the two<BR>\n" );
document.write( "b&#65289; How many outcomes are there in the sample space? <BR>\n" );
document.write( "c&#65289;What is the probability that the number formed ignoring the A and a subserpts) is i&#65289;235 (ii) greater than 300 (iii) odd (iv) a multiple of 5 and is greater than 300? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714757 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714757\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) The possible sequences of cards are listed below,<BR>\n" );
document.write( "distinguishing the ones labeled \"2\" by listing them as \"2A\" and \"2H\".<BR>\n" );
document.write( "2A 2H 3<BR>\n" );
document.write( "2A 2H 5<BR>\n" );
document.write( "2A 3 2H<BR>\n" );
document.write( "2A 3 5<BR>\n" );
document.write( "2A 5 2H<BR>\n" );
document.write( "2A 5 3<BR>\n" );
document.write( "2H 2A 3<BR>\n" );
document.write( "2H 2A 5<BR>\n" );
document.write( "2H 3 2A<BR>\n" );
document.write( "2H 3 5<BR>\n" );
document.write( "2H 5 2A<BR>\n" );
document.write( "2H 5 3<BR>\n" );
document.write( "3 2A 2H<BR>\n" );
document.write( "3 2A 5<BR>\n" );
document.write( "3 2H 2A<BR>\n" );
document.write( "3 2H 5<BR>\n" );
document.write( "3 5 2A<BR>\n" );
document.write( "3 5 2H<BR>\n" );
document.write( "5 2A 2H<BR>\n" );
document.write( "5 2A 3<BR>\n" );
document.write( "5 2H 2A<BR>\n" );
document.write( "5 2H 3<BR>\n" );
document.write( "5 3 2A<BR>\n" );
document.write( "5 3 2H<BR>\n" );
document.write( "There is a total of 24 listed sequences, because there are<BR>\n" );
document.write( "4 possibilities for the first card drawn,<BR>\n" );
document.write( "3 for the second one,<BR>\n" );
document.write( "and 2 for the third one,<BR>\n" );
document.write( "for a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A3%2A2=24=4%21 ALIGN=MIDDLE  ALT=\"4%2A3%2A2=24=4%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "b) If we can tell the cards listed as 2A and 2H,<BR>\n" );
document.write( "we would say there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible outcomes.<BR>\n" );
document.write( "If we cannot tell them apart,<BR>\n" );
document.write( "we would count <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible outcomes.<BR>\n" );
document.write( "There are half as many sequences of numbers, as sequences of cards,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > sequences  of numbers,<BR>\n" );
document.write( "because 2 will appear either once or twice in a sequence,<BR>\n" );
document.write( "and the first 2 to appear is as likely to be 2A as 2H.<BR>\n" );
document.write( " <BR>\n" );
document.write( "c) i) The probability that the number formed is 235 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12=2%2F24 ALIGN=MIDDLE  ALT=\"1%2F12=2%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because 235 is 1 of 12 possible sequences of numbers,<BR>\n" );
document.write( "or because 2 of the 24 sequences of cards,<BR>\n" );
document.write( "2A 3 5 and 2H 3 5 read as 235.<BR>\n" );
document.write( "ii) For a sequence to read as greater than 300,<BR>\n" );
document.write( "the first card drawn must be one of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards labeled 3 or 5,<BR>\n" );
document.write( "which constitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F4=1%2F2 ALIGN=MIDDLE  ALT=\"2%2F4=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the available cards,<BR>\n" );
document.write( "so the probability that the number formed is greater than 300 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "iii) For a sequence to read as an odd number,<BR>\n" );
document.write( "the last card must be odd.<BR>\n" );
document.write( "All <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards are equally likely to be the last card drawn,<BR>\n" );
document.write( "and exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > of them are labeled with an odd number (3 or 5),<BR>\n" );
document.write( "so the probability that the number formed is odd is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F4=1%2F2 ALIGN=MIDDLE  ALT=\"2%2F4=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "iv) As no card is labeled zero, the number formed will be a multiple of 5 if and only if the last card drawn is labeled 5.<BR>\n" );
document.write( "For that to happen with a number greater than 300, the first card must be labeled 3.<BR>\n" );
document.write( "That means that the sequence of numbers must be 325,<BR>\n" );
document.write( "or in other words that the middle card be labeled 2.<BR>\n" );
document.write( "That will happen in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible sequences of cards,<BR>\n" );
document.write( "and the sequence 3 2 5 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible sequences of numbers.<BR>\n" );
document.write( "As a consequence, the probability that the number formed<BR>\n" );
document.write( "is a multiple of 5<BR>\n" );
document.write( "and is greater than 300<BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F24=1%2F12 ALIGN=MIDDLE  ALT=\"2%2F24=1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );