document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010750>Question 1010750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains 8 red marbles, 4 white marbles, and 5 blue marbles. Find P(red and blue). (Don't just tell me the answer, show me your work!) </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "A bag contains 8 red marbles, 4 white marbles, and 5 blue marbles. Find P(red and blue).<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "We will assume that only two marbles are drawn from the bag, and hence there are two cases:<BR>\n" );
document.write( "A. The first marble is returned in the bag before drawing the second.<BR>\n" );
document.write( "B. The first marble is not returned in the bag before drawing the second.<BR>\n" );
document.write( "Let<BR>\n" );
document.write( "R=event of drawing a red<BR>\n" );
document.write( "B=event of drawing a blue.<BR>\n" );
document.write( "Therefore the successful events are RB or BR.<BR>\n" );
document.write( " <BR>\n" );
document.write( "A. First marble returned to the bag (with replacement).<BR>\n" );
document.write( "In this case, marbles are drawn with 8+4+5=17 in the bag.<BR>\n" );
document.write( "P(RB)=(8/17)*(5/17)=40/289 (multiplied because events are independent)<BR>\n" );
document.write( "P(BR)=(5/17)*(8/17)=40/289<BR>\n" );
document.write( "Probability of drawing BR or RB is<BR>\n" );
document.write( "P(RB or BR)=40/289+40/289=80/289 <BR>\n" );
document.write( "(probabilities are added because RB and BR are mmutually exclusive)<BR>\n" );
document.write( " <BR>\n" );
document.write( "B. First Marble not returned (without replacement).<BR>\n" );
document.write( "Here, for the first draw, there are 17 marbles in the bag, and only 16 marbles left in the second draw.<BR>\n" );
document.write( "P(RB)=(8/17)*(5/16)=40/272 (multiplied because events are independent)<BR>\n" );
document.write( "P(BR)=(5/17)*(8/16)=40/272<BR>\n" );
document.write( "Probability of drawing BR or RB is<BR>\n" );
document.write( "P(RB or BR)=40/272+40/289=80/272 <BR>\n" );
document.write( "(probabilities are added because RB and BR are mutually exclusive)<BR>\n" );
document.write( " </SPAN>\n" );
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