Percentage of smokers are females? Probability Question

Question

A workplace has 40% male employees. The company is concerned about the effect on health insurance premiums of the high smoking rates: 12% of employees are male smokers. Only 20% of smokers are female. What percentage of females are smokers?

I have tried many different things to solve this and am stuck. Thanks

Answer 1

Let the total number of employees be $x$, and the number of smokers be $s$, therefore,

1. number of male employees is $0.4x \Rightarrow$ the number of female employees is $0.6x$
2. number of male smokers is $0.12x$
3. number of female smokers is $0.2s$

Since the smokers are either male or female: $$ 0.12x + 0.2s = s $$ $$ 0.12x = 0.8s $$ The percentage of females are smokers is: $$ \frac{\text{# female smokers}}{\text{# females}} = \frac{0.2s}{0.6x} = \frac{0.25*0.8s}{0.6x} = \frac{0.25*0.12x}{0.6x} = 0.05 = 5\% $$