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What are the odds of getting a passing grade by sheer guessing here? (lemmy.world)

submitted 11 months ago* (last edited 11 months ago) by [email protected] to c/[email protected]

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Hi,

I just did a test which had two multiple choice questions. Each question was worth one point. Getting them both right would result in getting a 100% score. Suffice it to say, getting just one question right would give you 50% and with that a passing grade.

So you have two multiple choice questions. Both of which are unrelated to the other. Each question has four possible answers. When you finish the test. You get to have one more try. The questions and possible answers remain the same.

Let's say you use both tries and you remember your previous two respected answers. What would your odds be, if you were to brute force guess your way through this test, to get a passing grade or a 100%?

Edit: Both questions only have one correct answer.

IMPORTANT EDIT: YOU DO NOT KNOW WHICH ANSWER YOU HAD RIGHT OR WRONG THE SECOND TIME AROUND. You only know how many questions you got right. But you don't know which. Sorry for the confusion!

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[–] [email protected] 2 points 11 months ago* (last edited 11 months ago) (3 children)

~IIRC from my one stats class almost a decade ago, the math is pretty simple. If it’s truly a random guess then you have a 25% chance to get each question right, all you have to do is multiply them. (0.25)(0.25)=0.0625, you have a 6.25% of getting a 100. The other option to get a 50 is (0.25)(0.75)=0.1875, 18.75%. So there is a 75% chance of failing both.~

~If you get a second chance and can remember your two wrong answers, each problem now has only three options. To get each right, (0.33)(0.33)=0.1089, 10.89% chance. To get one right, (0.33)(0.67)=0.2211, 22.11% chance. 67% chance of failing both a second time.~

Something is amiss with my logic/math here but I’m too tired and am going to sleep now. With this logic, failing both the first time would be (0.75)(0.75)=0.5625 56.25%, the %s don’t add up to 100% so someone please correct me lol

[–] [email protected] 2 points 11 months ago

You only accounted for the situations with one correct answer in the case where it is the first question.

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