# Some doubts about conditional probability

Hi everyone, I’m studying the module about conditional probabilities.
Now, it’s clear that to formula to calculate is p(A|B) = p(A ∩B) / p(B)
So, if I understand correctly, p(A|B) is given by calculate the probability of A and B to happen divided by the probability of B.

Now I have the scheme

I know that by looking at the table p(M|L) = 32/90 but what if I use the formula?

so p(M ∩L) / p(L).
I know that p(A ∩B) = p(A) * p(B), so p(M ∩L) / p(L) = p(M)*p(L) / p(L) right?

Why do I get two different results? In fact one is 32/90 = 0.35… while the other is 0.2575

Could you please explain to me if I’m missing something?

P(A \cap B) = P(A)*P(B) is true only if A and B are independent events.

Do you think M and L are independent events based on the given information?

1 Like

Hmmmm…I would say they are independent, no?

Does the data support that?