document.write( "Question 946282: An urn contains 7 red, 5 blue, and 3 white marbles. You draw three marbles randomly without replacement. If the random variable R is defined to be the number of red marbles drawn, what is the expected value of R? \n" ); document.write( "

Algebra.Com's Answer #577330 by mathmate(429) $\"\"$ $\"About$

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\n" ); document.write( "Given
\n" ); document.write( "Urn contains 7 red, 5 blue and 3 white marbles for a total of 15.
\n" ); document.write( "Three are drawn without replacement.
\n" ); document.write( "Find expected number of marbles drawn.
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\n" ); document.write( "Solution
\n" ); document.write( "First we will need to find the probabilities of drawing 0, 1, 2 and 3 marbles.
\n" ); document.write( "P(0) = $\"8%2F15%2A7%2F14%2A6%2F13+=+8%2F65+\"$
\n" ); document.write( "P(1) = $\"3%2A%287%2F15%2A8%2F14%2A7%2F13%29+=+28%2F65+%29\"$
\n" ); document.write( "P(2) = $\"3%2A%287%2F15%2A6%2F14%2A8%2F13%29+=+24%2F65+\"$
\n" ); document.write( "P(3) = $\"7%2F15%2A6%2F14%2A5%2F13+=+5%2F65+\"$
\n" ); document.write( "Check: P(0)+P(1)+P(2)+P(3) = 1, checks.
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\n" ); document.write( "Next we will calculate the expected value of X = number of reds.
\n" ); document.write( "E[X] = Σ x*P(x) = $\"0%2A%288%2F65%29%2B1%2A%2828%2F65%29%2B2%2A%2824%2F65%29%2B3%2A%285%2F65%29+=+7%2F5+=+1.4\"$
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\n" ); document.write( "Answer
\n" ); document.write( "The expected number of red marbles drawn is 1.4 \n" ); document.write( "

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