document.write( "Question 715068: If we have a box containing slips of paper with the following numbers: 3,5,8,10,13,23,30,36,21,34 and a slip of paper is selected and not replaced. What are the following probabilities:
\n" ); document.write( "p(multiple of 3 then multiple of 5)
\n" ); document.write( "P(prime then odd)
\n" ); document.write( "P(prime then even then 21)
\n" ); document.write( "P(odd then 10 then 30)\r
\n" ); document.write( "\n" ); document.write( "How do you deal with numbers that share a common property (I.e. multiple of 5 and three, or odd and prime) in an independent probability problem like this one. \n" ); document.write( "

Algebra.Com's Answer #439211 by Edwin McCravy(20056) $\"\"$ $\"About$

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If we have a box containing slips of paper with the following numbers: 3,5,8,10,13,23,30,36,21,34 and a slip of paper is selected and not replaced. What are the following probabilities:
\n" ); document.write( "p(multiple of 3 then multiple of 5) =
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\r\n" );
document.write( "P(one of these 4, {3,30,36,21) AND THEN one of these 3 {5,10,30}.\r\n" );
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document.write( "This breaks into two cases each with a different probability:\r\n" );
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document.write( "Case 1:  We draw the 30 first  = \r\n" );
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document.write( "Case 2:  We don't draw 30 first  = \r\n" );
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document.write( "Desired probability =  =  \r\n" );
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\n" ); document.write( "P(prime then odd)
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\r\n" );
document.write( "P(one of these 4, {3,5,13,23) AND THEN one of these 5 {3,5,13,23,21}.\r\n" );
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document.write( "This breaks into two cases each with a different probability:\r\n" );
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document.write( "Case 1:  We draw the 21 second  = \r\n" );
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document.write( "Case 2:  We don't draw 21 second  = \r\n" );
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document.write( "Desired probability =  =  = \r\n" );
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document.write( "-------------------------------------\r\n" );
document.write( "

\n" ); document.write( "P(prime then even then 21)
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\r\n" );
document.write( "p(one of these 4, {3,5,13,23) AND THEN one of these 5 {8,10,30,36,34} and THEN {21}\r\n" );
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document.write( "None of these have a common property so it is not necessary to break into\r\n" );
document.write( "cases:\r\n" );
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document.write( "Desired probability =  =  = \r\n" );
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document.write( "-----------------------------------------\r\n" );
document.write( "

\n" ); document.write( "P(odd then 10 then 30)
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\r\n" );
document.write( "p(one of these 5, {3,5,13,23,21}. AND THEN {10} AND THEN {30}\r\n" );
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document.write( "None of these have a common property so it is not necessary to break into\r\n" );
document.write( "cases:\r\n" );
document.write( "\r\n" );
document.write( "Desired probability =  =  = \r\n" );
document.write( "

\n" ); document.write( "How do you deal with numbers that share a common property (I.e. multiple of 5 and three, or odd and prime) in an independent probability problem like this one.
\n" ); document.write( "

\r\n" );
document.write( "We have to break them into two or more cases, cases where we choose ones\r\n" );
document.write( "with the common properties, and cases where we don't.  Then add the probabilities.\r\n" );
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document.write( "Edwin

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