From this question: The probability that a student passes Math 31 is $\frac23$, and the probability that the student passes English is $\frac49$. If the probability of passing at least one course is $\frac45$, what is the probability that he passes both exam?
Then my teacher used the formula of addition rule by simply transposing the terms that become like this:
$$P(M\cap E) = P(M) + P(E) - P(M\cup E)$$
Note: Sorry for poor construction, i am writing this through mobile and having little access on some other tools.
My questions are:
why did my teacher used that formula instead of multiplication rule wherein we are looking for the probability of BOTH passing the exam? And
how to distinguish from the question what exact formula to use?