Correct me if I'm wrong, but...

[irnbru]

Even assuming what you said could actually happen it still isn't true.

If you studied 25% percent of a subject, and somehow got 25% of the questions right without guessing, and then guess on the rest, you still wouldn't hit 50%, and even if you did, 50% correct isn't likely to pass.

100 question exam, you know 25 answers, leaves 75 left. By guessing on the rest, you would get roughly 1 in 5 right. That's 15 more correct answers, for a total of 40 right out of 100. Fail?

Yes, fail.

Hey MA2,

Good job on the approximation. You are right that the average (mean) of guessing on 75 questions rounds to 15 questions. What this means though, is that only just over half of the people who guessed on the 75 questions would correctly guess at least 15 right.

The probability for guessing at least 25 answers correctly out of 75 is just less than 1 in 200.

It's interesting because when people start thinking about multiple events by depth, they tend to estimate based on a probability of 0.5 - equivalent to a coin toss - repeated. The actual probability in this case is less than 0.005.