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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)

There are a couple of errors, that I could spot, but I just woke up so my math might also be wrong hahaha.

(0.25)(0.25)=0.0625, you have a 6.25% of getting a 100.

Correct

The other option to get a 50 is (0.25)(0.75)=0.1875, 18.75%.

Almost, that's only true if the first one is the one you get right, but you can also get the second one right (3/4 * 1/4), meaning that it's double your answer, or 37.5% chance of getting at least one right.

So there is a 75% chance of failing both.~

56.25% as per above

~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.

That assumes you got both wrong the first time around.

To get one right, (0.33)(0.67)=0.2211, 22.11% chance. 67% chance of failing both a second time.~

Same as above, also same as getting the second one right.