3newton wrote
Quote:
Containers A and B each contain 8 gold coins, 12 silver coins, and nothing else. Container C contains 1 gold coin, 4 silver coins, and nothing else. A container is chosen at random and then a coin is chosen at random from that container. What is the probability that the chosen coin is silver?
A. 4/15
B. 2/5
C. 7/15
D. 3/5
E. 2/3
K_Leon wrote:
Does anyone think the question is quite misleading? Containers A and B "each" contains 8 gold coins, 12 silver coins, and nothing else. Does this not indicate that A contains 8G and 12S and that B contains the same coins as A? Only after I finish my calculation that I realized this way was wrong.
Yes. I remain confused. I got the correct answer through no fault of my own. I guessed.
A thorough discussion of "each" and "both" belongs in SC, so I'll keep it as short as I can. One hat I wear is editor of English prose.
"Each" refers to every one of any number, when considered individually or separately. "Both" refers to two, taken together. "Each," almost always, is a singular subject (hence singular verb). "Both" is a plural subject. The prompt's plural verb "contain" implies both. ????
"Each" should be used to emphasize the individuality of separate conditions. "The company gave both women $100,000." Unclear. Corrected: "The company gave each woman $100,000." (The women did not split the $100,000.)
Clarity would be simple to achieve. "Jars A and B both contain ..." Or "Jars A and B contain, respectively, 8 gold and 12 silver coins."
I still can't figure out how, in
3newton 's response, A has 0 silver coins
of 8 total but B has 12 silver coins
of 20 total. Doesn't A also have 20 coins?
If A = 8 total and B = 12 total, I think the equation is (1/3 * 0/8) + (1/3 * 12/12) + (1/3 * 4/5) = 3/5
kumarparitosh123 , I think you are correct.
If A and B both have 8 gold and 12 silver coins, I agree that the equation is (1/3 * 12/20) + (1/3 * 12/20) + (1/3 * 4/5) = 2/3
That said, if words were clear and OA were different, the content would be interesting.
3newton , are you sure the OA is correct?
chetan2u , I disagree respectfully. I don't think there's anything clear about it. Both answers D and E are defensible.
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