document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201706>Question 1201706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A closet contains 5 short-sleeve shirts and 3 long-sleeve shirts. Two shirts are chosen from the closet without looking. What is the probability that both shirts have short sleeves? </SPAN>\n" );
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document.write( "A student just learning about probability should be able to solve this problem by both of two basic probability methods.<br><BR>\n" );
document.write( "(1) Pick one shirt at a time....<br><BR>\n" );
document.write( "When picking the first shirt, there are 8 shirts, of which 5 are short sleeve.  The probability of getting a short-sleeve shirt on the first pick is 5/8.<br><BR>\n" );
document.write( "When picking the second shirt, there are 7 shirts left, of which 4 are short sleeve.  The probability of getting a short-sleeve shirt on the first pick is 4/7.<br><BR>\n" );
document.write( "The problem asks for the probability that the first shirt is short-sleeve AND the second shirt is short-sleeve.  The \"AND\" means the two probabilities must be multiplied to get the answer.<br><BR>\n" );
document.write( "ANSWER: (5/8)(4/7) = 20/56 = 5/14<br><BR>\n" );
document.write( "(2) Using \"n choose r\"....<br><BR>\n" );
document.write( "The number of ways of choosing any 2 of the 8 shirts is \"8 choose 2\": <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%288%2C2%29=%288%2A7%29%2F%282%2A1%29=28 ALIGN=MIDDLE  ALT=\"C%288%2C2%29=%288%2A7%29%2F%282%2A1%29=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The number of ways of choosing 2 of the 5 short-sleeve shirts is \"5 choose 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C2%29=%285%2A4%29%2F%282%2A1%29=10 ALIGN=MIDDLE  ALT=\"C%285%2C2%29=%285%2A4%29%2F%282%2A1%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The probability of getting two short-sleeve shirts is the number of ways of getting 2 short-sleeve shirts, divided by the total number of ways of choosing 2 of the 8 shirts: 10/28 = 5/14<br><BR>\n" );
document.write( "ANSWER: (again, of course...) 5/14<br><BR>\n" );
document.write( " </SPAN>\n" );
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