In a multiple choice question, there are five different answers, of which only one is correct. The probability that a student will know the correct answer is 0.6. If a student does not know the answer, he guesses an answer at random.
a) What is the probability that the student gives the correct answer?
b) If the student gives the correct answer, what is the probability that he guessed?
Let A$_1$ be: student knows the answer, A$_2$: student doesn't know the answer, B: student gives the correct answer
P(A$_1$) = 0.6 and P(A$_2$) = 0.4. How do I find P(B|A$_1$) and P(B|A$_2$)?