You take true/false test that has 60 questions.If you guess on each question, and have the same chance of guessing correct on each question, what is probability to get atleast 65% of questions correct

Answer 1

I think you have asked a question which does not have a definitive answer.

What you have asked, I believe, is equivalent to the following:

You have observed 60 binomial trials in which there were 39 (or more) successes.

What was the probability of success at each trial?

And the answer to that question is any probability of success at each trial is possible, but the lower the probability at each trial the less the probability of observing what you observed.