document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210425>Question 1210425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sara draws the 3 of hearts from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card.<BR>\n" );
document.write( "a. Determine the probability that the second card is another 3.<BR>\n" );
document.write( "P(3 3 of hearts) =<BR>\n" );
document.write( "b. Determine the probability that the second card is another heart.<BR>\n" );
document.write( "P (heart 3 of hearts) =<BR>\n" );
document.write( "c. Determine the probability that the second card is a club.<BR>\n" );
document.write( "P (club 3 of hearts) =<BR>\n" );
document.write( "d. Determine the probability that the second card is a 7.<BR>\n" );
document.write( "P(7 / 3 of hearts) =<BR>\n" );
document.write( "Write your answers as reduced fractions. </SPAN>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "(a)  <font color=red>1/17</font><BR>\n" );
document.write( "(b)  <font color=red>4/17</font><BR>\n" );
document.write( "(c)  <font color=red>13/51</font><BR>\n" );
document.write( "(d)  <font color=red>4/51</font>\r<BR>\n" );
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document.write( "Explanations\r<BR>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "There are 4 copies of cards with the label \"3\" (one for each suit).<BR>\n" );
document.write( "Since Sara is not replacing the 3 of hearts she selects, there are 4-1 = 3 copies remaining. This is out of 52-1 = 51 cards.\r<BR>\n" );
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document.write( "3/51 = (1*3)/(17*3) = <font color=red>1/17</font> is the probability of another 3 being selected if the first card is not replaced.\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "There are 52 cards in a deck. <BR>\n" );
document.write( "52/4 = 13 of which are hearts<BR>\n" );
document.write( "(ace, 2 through 10, jack, queen, king)<BR>\n" );
document.write( "This excludes jokers.\r<BR>\n" );
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document.write( "If 3 of hearts is the first card, and not put back or replaced, then there would be 13-1 = 12 hearts remaining out of 52-1 = 51 cards<BR>\n" );
document.write( "12/51 = (4*3)/(17*3) = <font color=red>4/17</font> is the answer to part (b)\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "There are 13 clubs out of 52-1 = 51 cards remaining.<BR>\n" );
document.write( "This leads directly to <font color=red>13/51</font> which cannot be reduced further.<BR>\n" );
document.write( "Note I did not subtract 1 from the clubs since the sets \"hearts\" and \"clubs\" are mutually exclusive. There's no overlap.\r<BR>\n" );
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document.write( "Part (d)\r<BR>\n" );
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document.write( "There are 4 copies of 7 out of 52-1 = 51 cards remaining.<BR>\n" );
document.write( "Therefore the answer is <font color=red>4/51</font><BR>\n" );
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