A manufacturing firm finds that 40 of its new hires turn out

A manufacturing firm finds that 40% of its new hires turn out to be good workers and 60% become poor workers. All current workers are given a reasoning test. Of the good workers, 90% pass it; 20% of the poor workers pass it. Assume that these figures will hold true in the future. If the company makes the test part of its hiring procedure and only hires people who meet the previous requirements and also pass the test, what percent of the new hires will turn out to be good workers? The percent of new hires that will be good workers is %. (Round to the nearest tenth.)

Solution

let the hires be x
good workers= 0.4x
poor workers=0.6x

good workers who pass=0.4x*0.9 = 0.36x
good workers who fail=0.04x

poor workers who pass=0.6x*0.2 = 0.12x
poor workers who fail=0.48x

new hires who are good workers and pass test=0.36x

Hence,answer=36%