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

submitted 10 months ago* (last edited 10 months ago) by FatTony@lemmy.world to c/asklemmy@lemmy.world

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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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[–] Hillock@kbin.social 2 points 10 months ago* (last edited 10 months ago)

Your calculations to get 100% are right but you are off for the 50% and. You are only considering one specific outcome. But it doesn't matter if the first question is wrong or the second so the chance is 0.250.75+0.750.25 which is 37.5 or double your answer. We can double check it by looking at it from the other direction.

The chance of failure is 0.75*0.75= 56.25%.

So there is a 43.75% of passing the first go around. Split between a 6.25% to get 100 and 37.5% to get 50.

Same mistake for the second calculations. 44.22% is the chance to get 50%