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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%.
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).
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).
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..................
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?
When I was writing questions for certification examinations, we were always careful to phrase the question such as, "Which one of the following is the best answer," not "What is the the correct answer." That may seem a small difference to some, but not when students who fail hire attorneys.
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..................
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.
A well formulated question, Pommie! Thanks for posting
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.
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.
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.
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.
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.
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%.
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%.
I can definitely see where you're coming from, but I don't agree. If all of them had the same value of 25%, then the chance would be 0%, because the correct answer is not listed (100%). You would need to take it further in order to realize that none of the given answers are correct. In fact, i don't believe there would be any correct answer (at all)--it is undefined.
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