document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199785>Question 1199785</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A jar contains 32 red marbles numbered 1 to 32 and 50 blue marbles numbered 1 to 50. A marble is drawn at random from the jar. Find the probability of the given event. Please enter reduced fractions.\r<BR>\n" );
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document.write( "(a) The marble is red. P(red)= <BR>\n" );
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document.write( "(b) The marble is odd-numbered. P(odd)= <BR>\n" );
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document.write( "(c) The marble is red or odd-numbered. P(red or odd) = <BR>\n" );
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document.write( "(d) The marble is blue or even-numbered. P(blue or even) =  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833753 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=833753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "32 red + 50 blue = 82 total<BR>\n" );
document.write( "P(red) = (number of red)/(number total)<BR>\n" );
document.write( "P(red) = (32)/(82)<BR>\n" );
document.write( "P(red) = (2*16)/(2*41)<BR>\n" );
document.write( "P(red) = 16/41\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>16/41</font>\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "R = set of red marbles labeled 1 to 32<BR>\n" );
document.write( "B = set of blue marbles labeled 1 to 50\r<BR>\n" );
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document.write( "R = {1,2,3,...,31,32}<BR>\n" );
document.write( "B = {1,2,3,...,49,50}\r<BR>\n" );
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document.write( "There are 32/2 = 16 odd values in set R.<BR>\n" );
document.write( "There are 50/2 = 25 odd values in set B.<BR>\n" );
document.write( "There are 16+25 = 41 odd values total.\r<BR>\n" );
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document.write( "41/82 = 1/2 of the values are odd.\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>1/2</font>\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "The notation n(A) refers to \"the number of items inside set A\".<BR>\n" );
document.write( "Example: A = {4,5,6} leads to n(A) = 3.\r<BR>\n" );
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document.write( "n(odd) = number of odd values<BR>\n" );
document.write( "n(odd) = 41<BR>\n" );
document.write( "This was calculated in part (b)\r<BR>\n" );
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document.write( "n(red) = number of red marbles<BR>\n" );
document.write( "n(red) = 32\r<BR>\n" );
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document.write( "n(red and odd) = 16<BR>\n" );
document.write( "This was calculated in part (b)\r<BR>\n" );
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document.write( "n(red or odd) = number of red or odd or both<BR>\n" );
document.write( "n(red or odd) = n(odd) + n(red) - n(red and odd) <BR>\n" );
document.write( "n(red or odd) = 41 + 32 - 16<BR>\n" );
document.write( "n(red or odd) = 57\r<BR>\n" );
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document.write( "Phrased another way: There are 32 red + 25 odd blue = 57 marbles that are red or odd or both.\r<BR>\n" );
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document.write( "P(red or odd) = n(red or odd)/n(total)<BR>\n" );
document.write( "P(red or odd) = 57/82\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>57/82</font>\r<BR>\n" );
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document.write( "Part (d)\r<BR>\n" );
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document.write( "n(blue) = 50<BR>\n" );
document.write( "n(even) = 41<BR>\n" );
document.write( "n(blue and even) = 25\r<BR>\n" );
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document.write( "n(blue or even) = n(blue) + n(even) - n(blue and even)<BR>\n" );
document.write( "n(blue or even) = 50 + 41 - 25<BR>\n" );
document.write( "n(blue or even) = 66\r<BR>\n" );
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document.write( "Put another way: There are 50 blue + 16 red even = 66 marbles that are blue or even or both\r<BR>\n" );
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document.write( "P(blue or even) = n(blue or even)/n(total)<BR>\n" );
document.write( "P(blue or even) = 66/82<BR>\n" );
document.write( "P(blue or even) = 33/41\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>33/41</font><BR>\n" );
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