A manufacturing firm finds that 8080% of its new hires turn out to be good workers and 20 %20% become poor workers. All current workers are given a reasoning test. Of the good workers, 9090% pass it; 4040% 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?

90%

Explanation:

Given that,

Percent of new hires turn out to be good workers = 80%

Percent of new hires turn out to be poor workers = 20%

Percent of good workers passed the reasoning test = 90%

Percent of bad workers passed the reasoning test = 40%

Probability of good workers who are passed:

= 0.8 × 0.9

= 0.72

Probability of poor workers who are passed:

= 0.2 × 0.4

= 0.08

Total probability:

= Probability of good workers who are passed + Probability of poor workers who are passed

= 0.72 + 0.08

= 0.80

Percent of the new hires will turn out to be good workers:

= Probability of good workers who are passed ÷ Total probability

= 0.72 ÷ 0.80

= 0.9 or 90%

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