Statistics question.

Random picks from set of correct answers is 25% in cases where there are 4 options. But what if 25% is listed twice as an option? Then random pick will be right 50% of the time, but if 50% is right, the chance of picking it at random is 25%... but if it's 25% then it's 50%, but if it's 50% then it's 25%.

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Ratchit said:

Pommie,

Well, let's take the answers one at a time. Suppose the correct answer is 25%. Then I have a 25% chance of selecting A which gives a value of 25%. Ditto for D. I have a 25% chance of selecting B which gives the wrong value of 60%. Ditto for C.

So my chances of selecting the correct choice is 25% (A and D). My chance of getting the correct answer is 50% (either A or D).

Ratch

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But then you'd need to find the answer that says 50%. But as Ron said, then it would be a 25% chance to get the right one, and it keeps going and going and going and going..................

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It is a probability question rather then a statistics problem.

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Ratchit said:

DerStrom8,



I have a 50% chance of selecting either A or D. Then I have a 50% chance of selecting specifically A or D. So, 50% times 50% is 25%.

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Where does it say that the correct answer is contained in the four options listed below or that one has to choose one of those options?

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Ratchit said:

japanhalt,



As long as there are only four choices, 25% has to be the correct answer.

Ratch

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I'm not quite sure I agree with that. Your chance of selecting either A or D is still 25% each. But the answer associated with each letter is the same, so you have a 50% chance of choosing 25% (2 out of the 4 would be correct), but then you get into the paradox--none of them are really correct. It just keeps going back and forth.

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Ratchit said:

DerStrom8,



Not really. I have a 50% chance of being correct, but only a 25% chance of selecting either A or D.

Ratch

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That's exactly what I was just saying. But then, if the answer is 50%, then the answer would be B. But then the chance of choosing that one would only be 25%, which goes back to where you started. The whole thing is just a catch-22--there is no "correct" answer. It's impossible to choose correctly. That's the whole point of this problem. I think Ron did a very good job of summing it up and explaining it, in post #5.

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Ratchit said:

DerStrom8,



If the answer were B at 50%, then you have a 25% chance of selecting it. Since there is no other answer of 50%, then there is no other "correct" answer. So the probability becomes 25% times 100%, which equals 25%. So B at 50% is the wrong answer. The same reasoning applies to C.

Ratch

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But if it's 50%, and you have a 25% chance, then the answer would be 25%. You don't see how it keeps going around in circles?

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Ratchit said:

DerStrom8,



No, I don't see it going around in circles. If B were the assumed correct choice, and it was to have a 25% chance of selection, but the value of B is 50%, then it cannot be the correct choice, and the assumption was false.

Let me put it another way, if all of A,B,C,D had the same value of 25%, then your chance of getting the correct answer would be 100%. But the chance of selecting a particular correct letter (A,B,C,D) would still be 25%.

Ratch

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