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. Survey ResultsContributeDo not contributeTotalMale118132250Female141109250Total259241500PrintDone EClick 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.)Enter your answer in each of the answer boxes.ave for LaterMacBook Air

Name: The accompanying table shows the results of a survey in which 250 male
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: 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. Survey ResultsContributeDo not contrib

Given: The 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: Contribute Do not contribute Total Male 118 132 250 Female 141 109 250 Total 259 241 500(a) Let X and Y be any two random variables. The conditional probability for X given Y is computed by the formula: P(X|Y)=P(X∩Y)P(Y) The probability that a randomly selected worker contributes to a retirement saving plan at work, given that the worker is male can be calculated as: P(Contribute|Male)=P(Contribute∩Male)P(Male)=118500250500=0.4720 Therefore, the probability that a randomly selected worker contributes to a retirement saving plan at work, given that the worker is male, is 0.472.(b) The probability that a randomly selected worker is female, given that the worker contributes to a retirement saving plan at work, can be calculated as: P(Female|Contribute)=P(Female∩Contribute)P(Contribute)=141500259500=0.5444 Therefore, the probability that a randomly selected worker is female, given that the worker contributes to a retirement saving plan at work, is 0.544.