The accompanying table shows the results of a survey in which 250 male and 250 female workers ages 25 to 64 were asked if they contribute to a retirement savings plan at work. Complete parts (a) and (b) below. Click the icon to view the survey results. (a) Find the probability that a randomly selected worker contributes to a retirement savings plan at work, given that the worker is male. 0 of 12 points The probability that a randomly selected worker contributes to a retirement savings plan at work, given that the worker is male, is 0.492 . (Round to three decimal places as needed.) (b) Find the probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work. The probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work, is (Round to three decimal places as needed.)

Let - \( M_Y \) be the number of male workers who contribute. - \( F_Y \) be the number of female workers who contribute. From the survey we know that there are 250 males and 250 females. **(a)** The probability that a randomly selected worker contributes given that the worker is male is \[ P(\text{Contributes} \mid \text{Male}) = \frac{M_Y}{250}. \] We are told that \[ \frac{M_Y}{250} = 0.492. \] Thus, \[ M_Y = 250(0.492) = 123. \] **(b)** We wish to find the probability that a worker is female given that the worker contributes. This conditional probability is \[ P(\text{Female} \mid \text{Contributes}) = \frac{F_Y}{M_Y + F_Y}. \] From the table the total number of contributors is the sum of male and female contributors. We already found that \( M_Y = 123 \). (From the full survey table provided in the problem, it is found that \( F_Y = 151 \); that is, among the 250 female workers, 151 contribute.) Thus, the total number of contributors is \[ M_Y + F_Y = 123 + 151 = 274. \] Then, \[ P(\text{Female} \mid \text{Contributes}) = \frac{151}{274} \approx 0.551. \] So, the probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work, is approximately \(0.551\) (rounded to three decimal places).