Solve the Problem $\frac { 1 } { 2 } \text {. }$

Multiple Choice

Solve the problem.
-In a certain population, the probability that a woman has red hair is $\frac { 1 } { 2 } \text {. }$ If a woman has red hair, the probability of her having freckles is $\frac { 5 } { 9 }$ If she does not have red hair, the probability of her having freckles is $\frac { 1 } { 10 } .$ If a woman is chosen at random from the population, what is the probability that she will have freckles?

A) $\frac { 59 } { 180 }$
B) $\frac { 1 } { 20 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 17 } { 45 }$