document.write( "Question 1149232: A urn contains 10 coins of which 4 are counterfeit. Coins are removed
\n" ); document.write( "from the urn, one at a time, until all counterfeit coins are found. If the
\n" ); document.write( "random variable X denotes the number of coins removed to find the first
\n" ); document.write( "counterfeit one, then what are the space and the probability density function
\n" ); document.write( "of X? \n" ); document.write( "
Algebra.Com's Answer #770573 by greenestamps(13200)\"\" \"About 
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\n" ); document.write( "X=1: You need to get a counterfeit on the first draw.
\n" ); document.write( "\"P%281%29+=+4%2F10\"

\n" ); document.write( "X=2: You need to get a genuine first and a counterfeit second.
\n" ); document.write( "\"P%282%29+=+%286%2F10%29%284%2F9%29\"

\n" ); document.write( "X=3: You need to get a genuine on the first two draws and a counterfeit on the third.
\n" ); document.write( "\"P%283%29+=+%286%2F10%29%285%2F9%29%284%2F8%29\"

\n" ); document.write( "Similarly....

\n" ); document.write( "\"P%284%29+=+%286%2F10%29%285%2F9%29%284%2F8%29%284%2F7%29\"
\n" ); document.write( "\"P%285%29+=+%286%2F10%29%285%2F9%29%284%2F8%29%283%2F7%29%284%2F6%29\"
\n" ); document.write( "\"P%286%29+=+%286%2F10%29%285%2F9%29%284%2F8%29%283%2F7%29%282%2F6%29%284%2F5%29\"
\n" ); document.write( "\"P%287%29+=+%286%2F10%29%285%2F9%29%284%2F8%29%283%2F7%29%282%2F6%29%281%2F5%29%284%2F4%29\"

\n" ); document.write( "Simplify as required to find the probability density function.

\n" ); document.write( "It is interesting to observe that the sum of all the probabilities is indeed 1.

\n" ); document.write( "The sample space is 1 to 7. Clearly if there are 6 genuine coins and 4 counterfeit coins, the \"worst case\" if you are trying to get a counterfeit coin is to draw all 6 of the genuine coins first, thus drawing the first counterfeit coin on the 7th draw.

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