document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181467>Question 1181467</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cookie jar has 3 red marbles and 1 white marble. A shoebox has 1 red marble and 1 white marble. Three marbles are chosen at random without replacement from the cookie jar and placed in the shoebox. Then 2 marbles are chosen at random and without replacement from the shoebox. What is the probability that both marbles chosen from the shoebox are red? </SPAN>\n" );
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document.write( "There are two ways to get 2 red marbles from the shoebox:<BR>\n" );
document.write( "(1) pick all 3 red (and 0 white) from the cookie jar and put in the shoebox; then choose 2 of the 4 red from among the 5 marbles in the shoebox; or<BR>\n" );
document.write( "(2) pick 2 red and the 1 white marble from the cookie jar and put in the shoebox; then choose 2 of the 3 red from among the 5 marbles in the shoebox.<br><BR>\n" );
document.write( "The probability for the first case is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%283%2C3%29%2FC%284%2C3%29%29%2A%28C%284%2C2%29%2FC%285%2C2%29%29+=+%281%2F4%29%286%2F10%29+=+6%2F40 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The probability for the second case is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28C%283%2C2%29%2AC%281%2C1%29%29%2FC%284%2C3%29%29%2A%28C%283%2C2%29%2FC%285%2C2%29%29+=+%283%2F4%29%283%2F10%29+=+9%2F40 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the probability of getting 2 red from the shoebox is 6/40+9/40 = 15/40 = 3/8.<br><BR>\n" );
document.write( "ANSWER: 3/8<br><BR>\n" );
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