Hi Grant,

You still have a loop there.

As you said,

There are 2 parts:

1) What is the answer?

2) What chance do I have of randomly selecting it?

Right. So if the question-master arbitrarily selects a solution, let's say 25%, he can present four options in which "25%" is only offered once.

i.e. the answer is 25%, and the chance of selecting it is 25%. The two numbers are the same, so there is no loop and the question is valid, answerable by circling the appropriate letter.

For example, these sets of options...

A) 25% I A) 50%

B) 30% I B) 50%

C) 60% I C) 60%

D) 80% I D) 80%

... are both valid. In the first case, the question-master's answersheet says that 25% is the right answer, so A is correct. In the second, the question-master's answersheet says that 50% is the right answer, so A or B is correct.

In both cases, the percentage figure on the question-master's answersheet matches the percentage figure circled by the student - AND mathematically the probabilities are correct - in the first case, the chance of randomly selecting A)25% is 25%, and so on.

The question does not say to use A, B, C or D in the answer.

But that's how multiple-choice exams work. You circle the letter. That method works for the valid questions above.

I believe the answer is "25%". (Which is the chance of selecting B. out of the 4 options.)

In which case you can circle the appropriate letter, either A or D, which both say the answer is 25%.

And if you do so, your answer will be wrong, because you've decided that the question-master's answersheet says that B)50% is the right answer. As you said:

25% would be the correct answer except it is represented twice, increasing your odds to 50%.

So I'd say the answer to the question is B (50% chance).

So, if you think the answersheet says B, circling A or D will obviously be the wrong answer.

But B would also be wrong, because it is evident that the chance of choosing it randomly is 25%, not 50%, therefore the question-master's answer is mathematically wrong, and he has set an invalid problem.

I'm getting dizzy...