document.write( "Question 976155: 1) There are two urns, one containing two white balls and four black balls, the other containing three white balls and nine black balls. One ball each is drawn out of the two urns. What is the probability of getting two balls of the same color?
\n" ); document.write( "(1) 7/12 (2) 1/24 (3) 1/12 (4) ½ \n" ); document.write( "

Algebra.Com's Answer #597817 by KMST(5328) $\"\"$ $\"About$

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You may have been taught about probability, but this is obvious common sense stuff that you can reason through without needing the thoughts and wisdom of anyone else. Supposedly the balls are indistinguishable by feel/touch, and you draw without looking, so each ball is equally likely to be picked. So, the probability of picking a white ball from one urn is the fraction of the balls in that urn that are white. The same goes for the probability of picking a black ball.
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\n" ); document.write( "The first urn described, containing two white balls and four black balls, has a total of $\"2%2B4=6\"$ balls.
\n" ); document.write( "The probabilities of getting a white or a black ball from that urn are
\n" ); document.write( " $\"P%5B1%5D\"$ $\"%28white%29=2%2F6=1%2F3\"$ and $\"P%5B1%5D\"$ $\"%28black%29=4%2F6=2%2F3\"$ .
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\n" ); document.write( "The second urn described, containing three white balls and nine black balls, has a total of $\"3%2B9=12\"$ balls.
\n" ); document.write( "The probabilities of getting a white or a black ball from that urn are
\n" ); document.write( " $\"P%5B2%5D\"$ $\"%28white%29=3%2F12=1%2F4\"$ and $\"P%5B2%5D\"$ $\"%28black%29=9%2F12=3%2F4\"$ .
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\n" ); document.write( "The drawing from one urn does not affect the outcome of the drawing from the other urn.
\n" ); document.write( "They are called \"independent events\" because of that, and to communicate with them,
\n" ); document.write( "you need your teachers or books tell you the vocabulary of their language.
\n" ); document.write( "Your teacher may have told you about multiplying probabilities when events are independent,
\n" ); document.write( "but you did not need to be told that, because common sense tells you that.
\n" ); document.write( "If $\"P%5B1%5D%28white%29=2%2F6=1%2F3\"$ , over many tries, you would expect to draw a white ball from the first urn $\"1%2F3\"$ of the times you did the experiment.
\n" ); document.write( "And for those times, in $\"1%2F4\"$ of those occasions you would draw a white ball from the second urn.
\n" ); document.write( "All in all, you would draw two white balls in $\"1%2F4\"$ of $\"1%2F3\"$ of the tries,
\n" ); document.write( "That is $\"%281%2F4%29%2A%281%2F3%29=1%2F12\"$ of the tries,
\n" ); document.write( "so the probability of getting two white balls is $\"1%2F12\"$ .
\n" ); document.write( "Through the same kind of reasoning, you realize that
\n" ); document.write( "the probability of getting two black balls is $\"%282%2F3%29%283%2F4%29=6%2F12=1%2F2\"$ .
\n" ); document.write( "In $\"1%2F12\"$ of the tries you would be expected to get two white balls, and
\n" ); document.write( "in $\"1%2F2=6%2F12\"$ of the tries you would be expected to get two black balls.
\n" ); document.write( "So in $\"1%2F12%2B6%2F12=7%2F12\"$ of the tries you would get two balls of the same color.
\n" ); document.write( "That means that the probability of getting two balls of the same color is $\"highlight%287%2F12%29\"$ . \n" ); document.write( "

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