Context: I’m always told on big tests that if I run out of time I should bubble all A’s or something because it’s a better chance I get it right than if I sporadically bubble answers. Why isn’t it just a consistent 25% chance?
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It is an even chance. But the variance is much lower. Most tests are intentionally written so that the answers get an evenly distribution of the choices. By picking the same answer for every question you know you are going to get a score of 25% given four choice for each question. But if you pick answers at random you might end up getting fewer correct answers by chance, or more correct answers.
Statistically, it’s a 25% chance outright that you’ll get the answer right by putting the same answer over and over. Whether the test is 10 questions or 200 questions, your chances are 25% overall each time. Random answers are 25% per question. So if the test is 10 questions, that 25% chance becomes 2.5% chance you’ll get the answer right overall. However the law of average dictates that they both will produce a very similar chance at a correct answer.
On the other hand. Statistically, you’re going to fail using either of these methods lol.
I’ve never heard this before. In theory, if the answers are evenly distributed then selecting all As should ensure that you’ll get 25% of them correct. Random guessing could give more or less correct answers, so I imagine this strategy is supposed to be a safe bet that you’ll get a few correct answers.
If the test has four questions for which the answers which are 1. A 2. B 3. C 4. D.
By picking C for every answer, you’re guaranteed 25%.
If you pick randomly for each one, there’s one chance in 256 that you’ll pick (A, B, C, D) and get 100%. And there’s one chance in 256 that you’ll pick (B, A, D, C), and get 0%. If you do this a bunch of times, your average score will still be 25%, but you will sometimes do better and sometimes do worse.
The longer the test, the more likely it is that the two strategies will give you very similar scores. So in practice it doesn’t make much of a difference.
If you have ABSOLUTELY no clue, and want to randomly guess, you should guess all of one letter because the test is engineered to have an even distribution of letters: you will get roughly 20% right if you guess all A’s, but could easily get 40% or 0% right if you do a pattern.
However, in reality, if you know anything about the subject, just looking at them and picking “your favorite” will have better odds than a total wild guess, even if you have no sensible idea about why the answer you like might be right.
**It’s not.**
The tests are written to have an approximately equal spread of answers, but that’s over the entire duration of the test not at every subgroup of 10 answers rolling through the test – and it is approximate.
If you’re at the last quarter of the test you have no way of knowing what the actual spread of remaining answers might be (unless you’re 100% confident of your previous answers and can then make a guess, and even then you won’t know for sure).
Checking all A is no more likely to net you more than 20% than randomly picking ABCDE. If it’s being marked by a human though they’re gonna immediately see where you ran out of time if the last 10 questions are all bubbled the same.
Better plan: Many multiple choice tests have at least one or two obvious dud answers. Very quickly rule out any obvious wrong answers – simple Eg: if the question is for multiplication and at least one number is even you can rule out any odd numbers from the answer, similar if both numbers are odd you can rule out any even numbers. If you can do this quickly you’ll boost your guess rate from approx 1 in 5 to ~1 in 3.
If both methods (random vs pick c for example) were tested a few times, hundred times, million billion times: any difference would be the result of chance (no matter how preposterous it feels) or some x factor like human error. Each choice, mathematically, is equal unless something specific is causing it to be different. Your question’s phrasing tells me you get it already. Your intuition says it shouldn’t make a difference but you have heard somewhere it does and feel like you are missing something. You were right all along, and probability is a difficult concept for most people.
You’re going to have less variance in your results if you go with a single letter rather than guessing all over.
Assuming a relatively even distribution of answers (i.e, 25% ±5%), if you guess the same letter, you’re going to get somewhere between 20-30% of the remaining answers correct. If you go random, you could theoretically get 100% correct, but you could also get 0% correct, with an average result of 25%.
It only sort of works if you do it for the whole test, not just one or two answers.
If you choose A on all questions it’s a guarantee that it will be the correct answer for those that have A as a solution (obviously). If there are roughly the same amount of A, B, C and D answers you’ll get around 25% of the questions.
If you go completely random you can potentially get all of them correct (but it’s very improbable) you can miss all of them, or anywhere in between.
Going for A all of them is a guaranteed ~25%.
This sounds like bad advice. First, it is almost certainly better to make an educated guess than a blind guess.
Second, if the goal is to maximise the chance of getting 25%, it probably won’t work.
There are two possibilities:
1. The letters are randomly distributed, and each question is independent of all others, in which case, it doesn’t matter at all what your strategy is, each guess is 25%.
2. There is some dependence between answers (eg, if there are three A’s in a row, then the chance of the next one being A is lower than 25%). In this case, there’s probably a better strategy than just picking A, but you don’t know what it is.
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