Question

In a company, the men who do not wear glasses are thrice as many as the men who do, while the women who do not wear glasses are ten more than the women who do. The probability that an employee wears glasses is 3/10. If selected employee wears glasses, the probability that this employee is a woman is 2/3. How many are the employees of the company?

Answer 1

if x and y are the men and women who wear glasses, then the total population is
x + 3x + y + y+10 = 4x+2y+10 = p

Now build up a probability tree. You get

(x+y)/p = 3/10
x = 3p/10 * 1/3
y = 3p/10 * 2/3

x=5, y=10, p=50
p(glasses) = x+y = 15/50 = 3/10
p(woman|glasses) = 10/15 = 2/3