In a search of $285$ asked people for the quality of a service the $130$ are men. The ones who are men and are satisfied from the quality are in percentage $30\%$ and the corresponding percentage for women is $25\%$.
Given that we have chosen a women which is the probability that she is satisfied.
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Suppose that "W" is the event "Woman", "M" the event "Man", "S" the event "Satisfied.
We want to calculate the conditional probability $P(S\mid W)=\frac{S\cap W}{P(W)}$, right?
We have that $P(W)=\frac{285-130}{285}=\frac{155}{130}$.
The point that I am confused is at the given information :
The ones who are men and are satisfied from the quality are in percentage $30\%$ and the corresponding percentage for women is $25\%$.
Is this the probability of intersection or is this the conditional probability?
"The ones who are men and are satisfied" is $P(M\cap S)$. And "the corresponding percentage" is $P(S\cap W) = 25\%$. Because the "and" specifies that this is not a conditional probability, it is the intersection of the events "being a man/woman" and "being satisfied".
Also, your $P(W)$ should be $\dfrac{155}{285}$, not $\dfrac{155}{130}$ :)
PS: Your Bayes' formula should be $P(S|W) = \dfrac{P(S\cap W)}{P(W)}$, not $P(S|W) = \dfrac{S\cap W}{P(W)}$ (which does not mean anything since $S\cap W$ is not a number, I'm assuming that was just a typo).