Question 1149775
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            The problem considers balls having different color and weight.

            The problem  MISSED  TO  SAY  that selection of any ball has  THE  SAME  probability,  independently of its weight and/or color.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I will assume it in my solution, &nbsp;although the problem is &nbsp;<U>silent</U> &nbsp;about this &nbsp;KEY &nbsp;ASSUMPTION.


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Let assume, for simplicity, that there are 1000 balls in the barrel, in all.


Then the number of black balls is 300; the number of white balls is 700.



The number of black balls weighting 1 oz is 0.3*300 = 90;

the number of white balls weighting 1 oz is 0.7*700 = 490.



The number of 1 oz balls, independently of their color, is 90 + 490 = 580, in all.



To calculate the probability under the problem's question, we should relate the number of black balls, 300, 
to the number of all 1 oz balls, which is 580 :


    P = {{{300/580}}} = {{{30/58}}} = 0.5172 = 51.72% approximately.    <U>ANSWER</Y>
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Solved.