Suppose there are two multiple choice questions with 4 choices each. Assume you answer the first question by choosing one of the four answer uniformly at random. You answer the second questions by choosing, again uniformly at random, one of the three answers you did not choose in the first question. What is the probability that you get the second question correctly?
The probability of getting question 2 correct seems dependent of what answer we choose for question 1.
Question 1: $\frac{1}{4}$
Question 2: $\frac{1}{3}$
Would the the probability of getting question 2 correct be $\frac{1}{4} \cdot \frac{1}{3} = \frac{1}{12}$?
How can we consider the possibility of the MC answer pick from the first question was the correct choice for the second question? Therefore making the probability of getting the second question zero.