Expert: Josh - 6/21/2004

Question
When answering a multichoice question on a test.  If the previous 5 answers were A's is it correct to assume that statisticly if i were to gues the answer to the next question that it would not be an A?

Answer
Hi Nick,

The answer is as follows. It depends on whether the questions are correlated or not. If the choices given for the answer are genuinely listed in random order, and all the questions are statistically uncorrelated (i.e., knowing what you have chosen before does not improve your chances of guessing the right answer) then, all choices for the next question are equally likely. That is, regardless of the history of previous selections, the correct answer for the next question could be anything.

However, the questions might be phrased in such a way that knowing the correct answer(s) to the previous question(s) may lead you to pick the right answer. That is, it may increase the likelihood of identifying the right answer for the next question. In this situation, we say that the questions are NOT INDEPENDENT, rather, the next question exhibits conditional dependence on the outcome of the previous question(s).

To summarize,
(1) In general, you cannot rule out that the answer to the next question will not be A again. Although in practice, the likelihood of such occurrence might be significantly diminished, if the choices are truly given in random order.
(2) The probability of making a correct guess depends on whether the answers are all equally likely (i.e., whether all answers are feasible and have been assigned randomly to a letter A,B,C or D, for instance.)
(3) Whether the history of past selections provides any clue as to what to pick next depends on whether the past questions convey any context information. The questions are not necessarily uncorrelated after all.

Cheers.