Question

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.
the probability that a randomly selected worker contributes to a retirement savings plan at work, given that the worker is male, is
(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.)

Explanation:

Step1: Recall conditional probability formula

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of part (a), if \(A\) is "contributes to retirement plan" and \(B\) is "is male", then \(P(A|B)=\frac{\text{Number of male contributors}}{\text{Total number of males}}\).

Step2: Calculate part (a)

For part (a), the number of male contributors is \(108\) and the total number of males is \(250\). So \(P=\frac{108}{250}= 0.432\).

Step3: Adjust formula for part (b)

For part (b), if \(A\) is "is female" and \(B\) is "contributes to retirement plan", then \(P(A|B)=\frac{\text{Number of female contributors}}{\text{Total number of contributors}}\).

Step4: Calculate part (b)

The number of female contributors is \(134\) and the total number of contributors is \(242\). So \(P=\frac{134}{242}\approx0.554\).

Answer:

(a) \(0.432\)
(b) \(0.554\)