Independent vs Dependent Events

[tullier.o]

From the 5 points, A,B,C,D and E on the number line above, 3 different points are to be randomly selected. What is the probability that the coordinates of the 3 points selected will all be positive?

In the diagram A and B are negative numbers and C,D and E are positive.
When I read this, I assumed that randomly selecting three points meant making three independent selections, one right after the other. That would've given me 3/5 * 3/5 * 3/5=27/125 (also assuming I can choose a number more than once).

Looking at the answer possibilities I realized my choice wasn't there so instead I approached it as if the three selections were happening simultaneously and therefore dependent selections, giving me 3/5*2/4*1/3=1/10 the correct answer.

I'm having trouble understanding how to know when events are independent or dependent. I get it when it's the sock drawer or bag of marbles examples, but in this case with a number line how could you assume that somehow they're choosing the three numbers at the exact same time and somehow they aren't allowed to select a number more than once?

If anyone could help clarify this or give some tips on these kinds of problems I'd really appreciate it, thanks!

[tommywallach]

Hey Tullier,

I don't think the language of dependent/independent is helpful (the GRE doesn't really use that language; there will never be a question that describes "dependent" events). Instead, notice the question said "different" points. That means you aren't allowed to choose the same point twice. That's really all you needed to see here.

Hope that helps!

-t