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Attached herewith is a spinning wheel. It's partitioned to equal 16 pieces and have four colors. Each color has 4 pieces which doesn't have an equal spread. That is, 4 green, 4 blue, 4 red and 4 yellow, but placed in different places.

My problem is, does probability of getting some color is 0.25? (I suppose no)

I personally have a feeling that, there's a high chance of getting red (according to this wheel) as it's spreaded all over the wheel.

Is my conclusion and the reasoning valid? Could you please explain if there's any misconception?

 image

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  • $\begingroup$ Given above is the link to the image as it's not attached properly $\endgroup$ – Dovini Jayasinghe Sep 10 at 5:15
  • $\begingroup$ The link requires permission. Use imgur maybe? $\endgroup$ – polettix Sep 10 at 5:40
  • $\begingroup$ @polettix Added the image. Thanks $\endgroup$ – Dovini Jayasinghe Sep 10 at 7:24
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    $\begingroup$ The chance of getting "some color" is, axiomatically, 1. The chance of getting some specified color equals the fraction of the circle's perimeter that color subtends, regardless of how the color is spread around. This is what it means for the spinner to be "fair" or "uniform"--that is, it doesn't favor or neglect any locations. $\endgroup$ – whuber Sep 10 at 12:59
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I'd start by ignoring the colors completely and asking: are the 16 slots totally equivalent as possible outcomes? Is there any that is more likely to come out, e.g. because it's bigger or some other slot is heavier or there's a bias in the way the wheel is spun?

If the answer is that the 16 slots are equiprobable, then each can come out with probability $\frac{1}{16}$. As a consequence, each possible group of 4 slots will get four times that probability, i.e. $\frac{1}{4} = 0.25$. Now you can re-add the colors.

Your intuition is that spreading the color in the wheel gives you better chances. But you're not placing guards in a territory, where they get a better view if they are spread evenly: each color still gets the same amount of the wheel.

When I look at the wheel and see those four red sections all alone I get the impression that there's a much higher chance that none of them will be selected. While there seems to be a lot of green there! So perceptions change from person to person, while hopefully the math is the same.

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  • $\begingroup$ Thank you so much. My guess here was, if we divide the circle into 4, each part consists or a red piece, but not all the colors occupy all the quadrants. That's why I'm misled do choose red as more likely to occur. $\endgroup$ – Dovini Jayasinghe Sep 10 at 10:45
  • $\begingroup$ Now the logic is understandable. Thanks a lot for helping $\endgroup$ – Dovini Jayasinghe Sep 10 at 10:45

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