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Interesting Probability Problem

Suppose you've a rectangle of \(1 \times 2\) unit squares area. If you start swiping a pointer over its perimeter through a knob switch, by turning it. What's the probability that when you stop(at random), you'd stop at any of the corner points of that rectangle? NOTE: I don't have the answer.

Note by Muhammad Abdullah
4 years, 2 months ago

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This is a great example of an interesting problem contributed by students, that is badly phrased and hence is rejected. The author has an opinion of what must happen, but fails to convey the proper meaning. The knob switch does something in his mind, but he fails to elucidate what that means. As such, there could be several interpretations of it.

Are we only restricted to the corners? It is not mentioned, and Bob's interpretation of the problem is valid.

How does the \(1 \times 2 \) squares come into play? It is not mentioned, and Aditya's interpretation of 'randomly stop on vertices' is valid. Calvin Lin Staff · 4 years, 2 months ago

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The answer is zero. The probability you land exactly on a point is zero, since there are an infinite amount of points in a line. Either that, or you've explained the problem incorrectly. Bob Krueger · 4 years, 2 months ago

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@Bob Krueger What if he meant that the knob switch lets you stop only on lattice points on the perimiter? Probability now is \( \frac{2}{3} \). Kenneth Chan · 4 years, 2 months ago

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@Kenneth Chan The issue with your interpretation is that the author explicitly says "Doesn't sound correct!" (see below).

I look at the further comment, and I seem to think that his objection is not valid, but I do not know for certain till it is clear what the knob does.

This is why he needs to explain clearly what the knob actually does. Calvin Lin Staff · 4 years, 2 months ago

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@Calvin Lin Knob is actually a device that helps us move pointer over the rectangle. That's it! Muhammad Abdullah · 4 years, 2 months ago

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@Bob Krueger i disagree, the probability tends to zero though, and hey, there's 4 vertices. Angel Leon · 3 years, 9 months ago

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i think an illustration of whatever you mean by "swiping a pointer over its perimeter through a knob switch" would help. No clue what this means. I'm imagining one of those toys where you draw with knobs Angel Leon · 3 years, 9 months ago

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1/4 Anurag Nayan · 4 years, 2 months ago

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@Anurag Nayan Explanation? Muhammad Abdullah · 4 years, 2 months ago

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I think it should be it should be 4/6 or 2/3. Aditya Parson · 4 years, 2 months ago

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@Aditya Parson Doesn't sound correct! Muhammad Abdullah · 4 years, 2 months ago

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@Muhammad Abdullah That means I have misinterpreted the working of the knob switch, if you could explain that. Aditya Parson · 4 years, 2 months ago

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@Aditya Parson Knob is not affecting the your answer. The point is that when you say 4/6, you're taking 6 as lengths and 4 as points. That ratio can't be said equal to probability. What's your view? Muhammad Abdullah · 4 years, 2 months ago

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