document.write( "Question 1103609: Suppose you have an urn containing 7 red and 3 blue balls. You draw three balls at random. On each draw, if the ball is red you set it aside and if the ball is blue you put it back in the urn. What is the probability that the third draw is blue? (If you get a blue ball it counts as a draw even though you put it back in the urn) \n" ); document.write( "

Algebra.Com's Answer #718293 by Edwin McCravy(20055) $\"\"$ $\"About$

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Suppose you have an urn containing 7 red and 3 blue balls. \r
\n" ); document.write( "\n" ); document.write( "You draw three balls at random. On each draw, if the ball is red
\n" ); document.write( "you set it aside and if the ball is blue you put it back in the
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\n" ); document.write( "you get a blue ball it counts as a draw even though you put it
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document.write( "The possible successful cases are\r\n" );
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document.write( "case 1. RRB\r\n" );
document.write( "case 2. RBB\r\n" );
document.write( "case 3. BRB\r\n" );
document.write( "case 4. BBB\r\n" );
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document.write( "-----\r\n" );
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document.write( "case 1. RRB\r\n" );
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document.write( "The probability of drawing a red first is 7/10\r\n" );
document.write( "Then you set it aside and the urn now contains 6 reds and 3 blues\r\n" );
document.write( "The probability of drawing a red second is 6/9 or 2/3\r\n" );
document.write( "Then you set it aside and the urn now contains 5 reds and 3 blues\r\n" );
document.write( "The probability of drawing a blue third is 3/8\r\n" );
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document.write( "So the probability for case 1 is (7/10)(2/3)(3/8) = 7/40\r\n" );
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document.write( "case 2. RBB\r\n" );
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document.write( "The probability of drawing a red first is 7/10\r\n" );
document.write( "Then you set it aside and the urn now contains 6 reds and 3 blues\r\n" );
document.write( "The probability of drawing a blue second is 3/9 or 1/3\r\n" );
document.write( "Then you put it back and the urn still contains 6 reds and 3 blues\r\n" );
document.write( "The probability of drawing a blue third is 3/9 or 1/3\r\n" );
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document.write( "So the probability for case 2 is (7/10)(1/3)(1/3) = 7/90\r\n" );
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document.write( "case 3. BRB\r\n" );
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document.write( "The probability of drawing a blue first is 3/10\r\n" );
document.write( "Then you put it back and the urn still contains 7 reds and 3 blues\r\n" );
document.write( "The probability of drawing a red second is 7/10 \r\n" );
document.write( "Then you set it aside and the urn now contains 6 reds and 3 blues\r\n" );
document.write( "The probability of drawing a blue third is 3/9 or 1/3\r\n" );
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document.write( "So the probability for case 2 is (3/10)(7/10)(1/3) = 7/100\r\n" );
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document.write( "case 4. BBB\r\n" );
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document.write( "The probability of drawing a blue first is 3/10\r\n" );
document.write( "Then you put it back and the urn still contains 7 reds and 3 blues\r\n" );
document.write( "The probability of drawing a blue second is 3/10 \r\n" );
document.write( "Then you put it back and the urn still contains 7 reds and 3 blues\r\n" );
document.write( "The probability of drawing a blue third is 3/10 \r\n" );
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document.write( "So the probability for case 4 is (3/10)(3/10)(3/10) = 27/1000\r\n" );
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document.write( "----\r\n" );
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document.write( "So the final probability is the sum of those 4 probabilities:\r\n" );
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document.write( "7/40 + 7/90 + 7/100 + 27/1000 = 787/2250\r\n" );
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document.write( "That's about 0.34977777...\r\n" );
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document.write( "Edwin

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