## Probability for getting points from guessed answers.

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retrospectacles
Posts: 3
Joined: Sat Aug 18, 2012 4:55 pm

### Probability for getting points from guessed answers.

So, I thought it would be fun to actually calculate the probability of getting any points for guessed answers and share it with you all.

The probability of getting completely guessed answers right on the physics GRE follows a binomial distribution, with n being the # of questions you are guessing on, k being the # of question you get right, and p being the probability of guessing a correct answer on any one question.

So let's say you're running out of time and still have 15 questions to answer. If you get only 3 of those 15 questions right, you break even, i.e. you will get 0 points total for answering those 15 questions, and you did a bunch of circling for nothing. Any more than 3 questions right and you will score some positive points, while any less than 3 questions right and you will score negative points.

Let's say you don't eliminate any answers as you're guessing. That mean p = 0.2.

So, from the binomial distribution,

P(X > 3) ~ 0.35
P(X < 3) ~ 0.40

So in this case, it probably wouldn't be worth it to guess. you have a 40% of losing points by guessing, and only 35% to actually gain any points.

If you eliminate one obviously wrong answer from all 15 of the questions, then p = 0.25.
Again,

P(X > 3) ~ 0.54
P(X < 3) ~ 0.24

OK, it's better, but the odds still wouldn't make me feel comfortable guessing. A 1/4 chance on actually losing points does not sound appealing.

If we're able to eliminate 2 obviously incorrect answers for all those 15 questions, then p changes again to p = 0.333333. Now guessing starts being worth it….

P(X > 3) ~ 0.79
P(X < 3) ~ 0.08

An 80% of getting some plus points and only an 8% of getting negative points starts looking good to me now. Of course, to get to this point, you'd need to eliminate 2 answers on all 15 of those unanswered questions, which would take some time. If you're already considering guessing as an option, you're probably a little strained for time, and not be be able to be so thorough.

bfollinprm
Posts: 1203
Joined: Sat Nov 07, 2009 11:44 am

### Re: Probability for getting points from guessed answers.

retrospectacles wrote:So, I thought it would be fun to actually calculate the probability of getting any points for guessed answers and share it with you all.

The probability of getting completely guessed answers right on the physics GRE follows a binomial distribution, with n being the # of questions you are guessing on, k being the # of question you get right, and p being the probability of guessing a correct answer on any one question.

So let's say you're running out of time and still have 15 questions to answer. If you get only 3 of those 15 questions right, you break even, i.e. you will get 0 points total for answering those 15 questions, and you did a bunch of circling for nothing. Any more than 3 questions right and you will score some positive points, while any less than 3 questions right and you will score negative points.

Let's say you don't eliminate any answers as you're guessing. That mean p = 0.2.

So, from the binomial distribution,

P(X > 3) ~ 0.35
P(X < 3) ~ 0.40

So in this case, it probably wouldn't be worth it to guess. you have a 40% of losing points by guessing, and only 35% to actually gain any points.

If you eliminate one obviously wrong answer from all 15 of the questions, then p = 0.25.
Again,

P(X > 3) ~ 0.54
P(X < 3) ~ 0.24

OK, it's better, but the odds still wouldn't make me feel comfortable guessing. A 1/4 chance on actually losing points does not sound appealing.

If we're able to eliminate 2 obviously incorrect answers for all those 15 questions, then p changes again to p = 0.333333. Now guessing starts being worth it….

P(X > 3) ~ 0.79
P(X < 3) ~ 0.08

An 80% of getting some plus points and only an 8% of getting negative points starts looking good to me now. Of course, to get to this point, you'd need to eliminate 2 answers on all 15 of those unanswered questions, which would take some time. If you're already considering guessing as an option, you're probably a little strained for time, and not be be able to be so thorough.
This isn't the statistic you want. What you want is the probability that guessing those answers assists you in getting into a school you otherwise wouldn't vs. the probability that guessing results in a score that will prevent you from getting in to a school you otherwise would. This could be reasonably proxied by considering the probability that guessing takes you above or below some threshold(s), which means the answer of the question "should I guess?" is dependent on your expected score from the other 80ish questions.