# Interpretation of fitted probabilites in binary logistic regression [duplicate]

I run a simple binary logit regression with a single dummy as IV. The output gives log odds and is:

Intercept: 0.3045
Female: 0.4521

Calculating the odds ratio for female is $$exp(0.4521) = 1.572$$ and I usually interpret it like this: "If the person is female, this multiplies the odds of Y = 1 by 1.572."

I was now interested in the probability and couldn't get my head around it. First I calculated the probability from the OR for female, which is $$\frac{1.572}{1+1.572} = 0.61$$. I thought it translates into something like: "If the person is female, the probability of Y = 1 increases by 61%". However, when calculating the fitted probability of Y = 1 | female and Y = 1 | male I get:

$$\frac{exp(0.3045+0.4521)}{1+exp(0.3045+0.4521)} = 0.681$$ for female and $$\frac{exp(0.3045)}{1+exp(0.3045)} = 0.576$$ for male.

This is clearly no increase by 61% from male to female.

My question: How does the probability of 0.61, calculated above, relate to the fitted probabilities? Did I do anything wrong?

Cheers!