There are 66 employees in a certain firm. We know that 36 of these employees are men, 4 of these men are secretaries, and 19 secretaries are employed by the firm. What is the probability that an employee chosen at random is a secretary, given that the employee is a woman? The probability is \( \square \). Type a simplified fraction.)

To find the probability that a randomly chosen employee is a secretary, given that the employee is a woman, we first need to determine the number of women and the number of women who are secretaries. 1. Total employees = 66. 2. Total men = 36, so total women = 66 - 36 = 30. 3. Total secretaries = 19. 4. Secretaries who are men = 4, so secretaries who are women = 19 - 4 = 15. Now we can calculate the probability that a randomly chosen employee is a secretary given that the employee is a woman: \[ P(\text{Secretary | Woman}) = \frac{\text{Number of women secretaries}}{\text{Total number of women}} = \frac{15}{30} = \frac{1}{2}. \] So, the probability is \( \frac{1}{2} \).