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~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
Edit 2: thanks for the corrections everyone, I forgot that the order does matter in this equation
There are a couple of errors, that I could spot, but I just woke up so my math might also be wrong hahaha.
Correct
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.
56.25% as per above
That assumes you got both wrong the first time around.
Same as above, also same as getting the second one right.
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%
You only accounted for the situations with one correct answer in the case where it is the first question.