document.write( "Question 824196: a bag contains 4red,5white and 7bllack balls.if 2 balls are taken random,what is the probability that both of them will be black or both will be white? \n" ); document.write( "
Algebra.Com's Answer #496161 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "YOUR PROBLEM:\r\n" );
document.write( "A bag contains 4 red, 5 white and 7 black balls. If 2 balls are taken random, what is the \r\n" );
document.write( "probability that both of them will be black or both will be white?\r\n" );
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document.write( "SOLUTION:\r\n" );
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document.write( "First, find the probability that two balls will be black. There are 16 balls altogether. Of these, \r\n" );
document.write( "7 of them are black and 9 are not black. Count the possible ways of choosing two black balls \r\n" );
document.write( "and 0 non-black balls from the bag (combinations because order doesn't matter):\r\n" );
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document.write( "There are 7C2 ways to choose two black balls = 21\r\n" );
document.write( "There are 9C0 ways to choose zero non-black balls = 1\r\n" );
document.write( "There are 16C2 ways to draw any two balls = 120\r\n" );
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document.write( "The probability of drawing two black balls is (7C2)(9C0)/(16C2) = (21)(1)/120 = 21/120\r\n" );
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document.write( "Second, find the probability that both balls will be white. There are 16 balls altogether. Of \r\n" );
document.write( "these, 5 are white and 11 are not white. Count the possible ways of choosing two white balls\r\n" );
document.write( "and 0 non-white balls from the bag:\r\n" );
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document.write( "There are 5C2 ways to choose two white balls = 10\r\n" );
document.write( "There are 11C0 ways to choose zero non-white balls = 1\r\n" );
document.write( "There are 16C2 ways to draw any two balls = 120\r\n" );
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document.write( "The probability of drawing two white balls is (5C2)(11C0)/(16C2) = (10)(1)/120 = 10/120\r\n" );
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document.write( "We want the probability that you will draw two black OR two white, so we add these probabilities.\r\n" );
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document.write( "21/120 + 10/120 = 31/120\r\n" );
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document.write( "I hope this helps! Feel free to emil me if you have questions about this explanation.\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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