SOLUTION: Use base therim 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

Algebra ->  Probability-and-statistics -> SOLUTION: Use base therim 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       Log On


   

Question 1149775: Use base therim
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?
Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
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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.
            I will assume it in my solution,  although the problem is  silent  about this  KEY  ASSUMPTION. 


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%2F580 = 30%2F58 = 0.5172 = 51.72% approximately.    ANSWER

Solved.