document.write( "Question 1149775: Use base therim
\n" ); document.write( "A barrel contains black and white balls. 30% of the balls are black. Also 30% of the black balls weight 1oz. and 70% of the white balls weigh 1oz. If a 1oz ball is randomly selected what is the probability that the ball is black? \n" ); document.write( "

Algebra.Com's Answer #771108 by ikleyn(52863) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "            The problem considers balls having different color and weight.\r
\n" ); document.write( "\n" ); document.write( "            The problem MISSED TO SAY that selection of any ball has THE SAME probability, independently of its weight and/or color.\r
\n" ); document.write( "\n" ); document.write( "            I will assume it in my solution, although the problem is silent about this KEY ASSUMPTION.\r
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document.write( "Let assume, for simplicity, that there are 1000 balls in the barrel, in all.\r\n" );
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document.write( "Then the number of black balls is 300; the number of white balls is 700.\r\n" );
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document.write( "The number of black balls weighting 1 oz is 0.3*300 = 90;\r\n" );
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document.write( "the number of white balls weighting 1 oz is 0.7*700 = 490.\r\n" );
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document.write( "The number of 1 oz balls, independently of their color, is 90 + 490 = 580, in all.\r\n" );
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document.write( "To calculate the probability under the problem's question, we should relate the number of black balls, 300, \r\n" );
document.write( "to the number of all 1 oz balls, which is 580 :\r\n" );
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document.write( "    P =  =  = 0.5172 = 51.72% approximately.    ANSWER\r\n" );
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