document.write( "Question 430559: There are two sets of marbles. Both have 1,000 in them. Bag 1 has 700 blue and 300 red. Bag 2 has 300 blue and 700 red. Picking a bag at random you draw out 10 marbles with replacement. If 7 are red and 3 are blue, what is the exact probability of you picking Bag 1? \n" ); document.write( "

Algebra.Com's Answer #299013 by Edwin McCravy(20056) $\"\"$ $\"About$

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There are two sets of marbles. Both have 1,000 in them. Bag 1 has 700 blue and 300 red. Bag 2 has 300 blue and 700 red. Picking a bag at random you draw out 10 marbles with replacement. If 7 are red and 3 are blue, what is the exact probability of you picking Bag 1?
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document.write( "                      P(bag1 & 7R3B)     \r\n" );
document.write( "P(bag1 given 7R3B) = ----------------  \r\n" );
document.write( "                         P(7R3B)\r\n" );
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document.write( "P(7R3B|bag1) = C(10,3)[(.7)^7(.3)^3] \r\n" );
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document.write( "P(7R3B|bag2) = C(10,3)[(.3)^7(.7)^3] \r\n" );
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document.write( "Numerator = P(bag1 & 7R3B) = P(bag1)*P(7R3B|bag1) = (.5)C(10,3)(.7)^7(.3)^3\r\n" );
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document.write( "Denominator = P(7R3B) = P[(bag1 & 7R3B) OR (bag2 & 7R3B)] = \r\n" );
document.write( "             (.5)C(10,3)[(.7)^7(.3)^3] + (.5)C(10,3)[(.3)^7(.7)^3]\r\n" );
document.write( "  \r\n" );
document.write( "Numerator = P(Bag2 & 7R3B) = P(Bag2)*P(7R3B|Bag2) = (.5)C(10,3)(.3)^7(.7)^3\r\n" );
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document.write( "              (.5)C(10,3)(.7)^7(.3)^3\r\n" );
document.write( "-----------------------------------------------------\r\n" );
document.write( "(.5)C(10,3)[(.7)^7(.3)^3] + (.5)C(10,3)[(.3)^7(.7)^3]\r\n" );
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document.write( "Divide top and bottom by (.5)C(10,3)\r\n" );
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document.write( "        (.7)^7(.3)^3\r\n" );
document.write( "-----------------------------\r\n" );
document.write( " (.7)^7(.3)^3 + (.3)^7(.7)^3\r\n" );
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document.write( "Divide the top and bottom by (.7)^3(.3)^3\r\n" );
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document.write( "        (.7)^4\r\n" );
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document.write( "   (.7)^4 + (.3)^4\r\n" );
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document.write( "Multiply top and bottom by 10^4\r\n" );
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document.write( "         7^4\r\n" );
document.write( "    -------------\r\n" );
document.write( "      7^4 + 3^4\r\n" );
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document.write( "        2401\r\n" );
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document.write( "      2401 + 81 \r\n" );
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document.write( "        2401\r\n" );
document.write( "       ------\r\n" );
document.write( "        2482\r\n" );
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document.write( "Edwin

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