document.write( "Question 169548: Three cards are drawn from a deck without replacement. The number of aces is counted. The expected value of the random variable in the experiment is:\r
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Algebra.Com's Answer #125027 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "X = no. of aces drawn which can either be 0, 1, 2, or 3.\r\n" );
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document.write( "So make this chart:\r\n" );
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document.write( "Now we must calculate the probabilities to go in\r\n" );
document.write( "the bottom row of the chart.\r\n" );
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document.write( "We first calculate the probability of getting 0 aces.\r\n" );
document.write( "This means we draw 3 non-aces.  There are 48 non-aces.\r\n" );
document.write( "So the number of ways to choose three non-aces is\r\n" );
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document.write( "The denominator is \r\n" );
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document.write( "So the probability of getting 0 aces is \r\n" );
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document.write( "Next we calculate the probability of getting 1 ace.\r\n" );
document.write( "This means we draw 2 non-aces and 1 ace. There are \r\n" );
document.write( "48 non-aces. So the number of ways to choose two \r\n" );
document.write( "non-aces is  and the number of ways to\r\n" );
document.write( "choose the ace is  ways.  That's \r\n" );
document.write( " ways.\r\n" );
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document.write( "The denominator again is \r\n" );
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document.write( "So the probability of getting exactly 1 ace is \r\n" );
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document.write( "Next we calculate the probability of getting \r\n" );
document.write( "exactly 2 aces. This means we draw 1 non-ace and \r\n" );
document.write( "2 ace3. There are 48 non-aces. So the number of \r\n" );
document.write( "ways to choose one non-aces is  and \r\n" );
document.write( "the number of ways to choose 2 aces is  \r\n" );
document.write( "ways.  That's \r\n" );
document.write( " ways.\r\n" );
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document.write( "The denominator is as before \r\n" );
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document.write( "So the probability of getting exactly 2 aces is \r\n" );
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document.write( "Finally we calculate the probability of getting 3 aces.\r\n" );
document.write( "The number of ways to choose 3 aces is  ways.  \r\n" );
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document.write( "The denominator is \r\n" );
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document.write( "So the probability of getting exactly 3 aces is \r\n" );
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document.write( "So we fill in the chart:\r\n" );
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document.write( "Now to find the expectation, we add the products of each\r\n" );
document.write( "value of x times its probability:\r\n" );
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document.write( "That rounds to choice C, \r\n" );
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document.write( "Edwin

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