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Two persons arrive at train station independently of each other at random times between 1 PM and 1:30 PM. What is the probability that one will arrive between 1 PM and 1:12 PM and the other between 1:17 PM and 1:30? Why is $$\displaystyle \frac{12}{30}\frac{13}{30}$$ a wrong answer?

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Do you mean that I have to multiply by $$\displaystyle 2$$? $$\displaystyle \frac{12}{30}\frac{13}{30}$$x$$\displaystyle 2$$
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p(that one will arrive between 1 PM and 1:12 PM and the other between 1:17 PM and 1:30) = p(Joan will arrive between 1 PM and 1:12 PM and Jack will arrive between 1:17 PM and 1:30 OR Jack will arrive between 1 PM and 1:12 PM and Joan will arrive between 1:17 PM and 1:30) = ..... Continue.
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george357 said: Even if you switch their names, we will get the same answer because we have a multiplication here. Click to expand... Good! So what is the probability that one will arrive between 1 PM and 1:12 PM and the other between 1:17 PM and 1:30?
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Even if you switch their names, we will get the same answer because we have a multiplication here.
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george357 said: $$\displaystyle \frac{13}{30}\frac{12}{30}$$ Both are the same but yours the names were known! [/QUOTEIf both are the same why didn't you get the same answer??????? So what would he probability be if I switch the their names? That is, what is the probability that Jack will arrive between 1 PM and 1:12 PM and Jane between 1:17 PM and 1:30? Click to expand...
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Jomo said: OK, I'll accept any answer. Now can you explain how you got this answer? How should the answer to my question and the original question relate to one another? Click to expand... $$\displaystyle \frac{13}{30}\frac{12}{30}$$ Both are the same but yours the names were known!
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george357 said: $$\displaystyle \frac{13}{75}$$ Click to expand... OK, I'll accept any answer. Now can you explain how you got this answer? How should the answer to my question and the original question relate to one another?
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Jomo said: Hint: What is the probability that Jane will arrive between 1 PM and 1:12 PM and Jack between 1:17 PM and 1:30? Click to expand... $$\displaystyle \frac{13}{75}$$
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Hint: What is the probability that Jane will arrive between 1 PM and 1:12 PM and Jack between 1:17 PM and 1:30?
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