I'm currently trying to solve this probability question and I'm quite unsure if my answer is correct or not.
On a multiple-choice exam, there are $100$ questions each with $4$ possible choices.
A student is certain of the correct answer to each question with probability $0.6$ and guesses randomly among the $4$ choices otherwise.
i. What is the probability that the student correctly answers question #$1$?
ii. What is the probability that the student was certain of the answer to question #$1$ given that they got it correct?
I think I might be a bit off.
Can anyone tell me if my calculations are correct?