document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197574>Question 1197574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two marbles are drawn randomly one after the other without replacement from a jar that contains 9 red marbles, 9 white marbles, and 3 yellow marbles. Find the probability of the following events.\r<BR>\n" );
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document.write( "(a) A red marble is drawn first followed by a white marble.<BR>\n" );
document.write( "The probability is:\r<BR>\n" );
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document.write( "(b) A white marble is drawn first followed by a white marble.<BR>\n" );
document.write( "The probability is:\r<BR>\n" );
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document.write( "(c) A yellow marble is not drawn at all.<BR>\n" );
document.write( "The probability is: </SPAN>\n" );
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document.write( "These are very basic probability problems.  You need to know two things:<br><BR>\n" );
document.write( "(1) The probability of an event with discrete outcomes is the ratio of the number of \"good\" outcomes to the total number of possible outcomes.<br><BR>\n" );
document.write( "(2) The probability of a particular sequence of outcomes is the product of the probabilities of each.<br><BR>\n" );
document.write( "(a) A red marble is drawn first followed by a white marble.<BR>\n" );
document.write( "Tranlsation: A red marble first AND a white marble second.<BR>\n" );
document.write( "P(red marble first): 9+9+3=21 marbles, 9 red marbles, so 9/21 = 3/7<BR>\n" );
document.write( "P(white marble second): 8+9+3=20 marbles, 9 white marbles, so 9/20<BR>\n" );
document.write( "P(red then white) = (3/7)(9/20) = 27/140<br><BR>\n" );
document.write( "(b) A white marble is drawn first followed by a white marble.<BR>\n" );
document.write( "Tranlsation: A white marble first AND a white marble second.<BR>\n" );
document.write( "P(white marble first): 9+9+3=21 marbles, 9 white marbles, so 9/21 = 3/7<BR>\n" );
document.write( "P(white marble second): 9+8+3=20 marbles, 8 white marbles, so 8/20 = 2/5<BR>\n" );
document.write( "P(white then white) = (3/7)(2/5) = 6/35<br><BR>\n" );
document.write( "(c) A yellow marble is not drawn at all.<BR>\n" );
document.write( "Tranlsation: A red or white marble first AND a red or white marble second.<BR>\n" );
document.write( "P(red or white marble first): 9+9+3=21 marbles, 9+9=18 red or white marbles, so 18/21 = 6/7<BR>\n" );
document.write( "P(red or white marble second): 9+8+3=20 marbles, 9+8=17 red or white marbles, so 17/20<BR>\n" );
document.write( "P(red or white then red or white) = (6/7)(17/20)=51/70<br><BR>\n" );
document.write( " </SPAN>\n" );
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