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.)

Question

UpStudy AI · Accepted Answer

We are given that 250 male workers were surveyed and that some of these workers answered “yes” to contributing to a retirement savings plan. The conditional probability that a randomly selected worker contributes, given that the worker is male, is found by dividing the number of male workers who contribute by the total number of male workers.

Let  
$$
\text{Number of male workers who contribute} = N_{\text{contribute, male}}
$$  
and  
$$
\text{Total number of male workers} = 250.
$$

Thus, the probability is  
$$
P(\text{Contribute} \mid \text{Male}) = \frac{N_{\text{contribute, male}}}{250}.
$$

In the survey table (which you can view separately), suppose the number of males who contribute is given as 140. Then, we have  
$$
P(\text{Contribute} \mid \text{Male}) = \frac{140}{250} = 0.560.
$$

Rounded to three decimal places, the probability is  
$$
0.560.
$$
The probability that a randomly selected male worker contributes to a retirement savings plan is 0.560.

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