Conditional probability using Bayes

Question

Assume that 45% of total population is male and 55% are female
The population is classified based on feature hair as :

                    Male             Female
Long Hair           25%               95%
Short Hair          75%               5%

Give that a person has long hair what's the probability that the person is a female
I have come up with the following solution. It seems tricky so not sure if it's correct
or there is an easier way to do it

My Solution:
Let p be the total population. then males = .45 * p and females = .55 * p
we have to find P(f|lh) = p(lh|f) * P(f)/P(lh)

P(lh|f) = .95 and P(f) = .55
P(lh) = .45 * .25 + .55 * .95
so P(f|lh) =
.95 * .55
------------------------
.45 * .25 + .55 * .95

Is that a correct way to approach this problem?

Answer 1

A:being long hair female

B:being long hair

$$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{55\% \times 95\%}{45\%\times 25\% + 55\%\times 95\%}$$