A firm is accustomed to training operators who do certain tasks on a production line. those operators who attend the training course are known to be able to meet their production quotas 90% of the time. new op - erators who do not take the training course only meet their quotas 65% of the time. fifty percent of new op - erators attend the course. given that a new operator meets her production quota, what is the probability that she attended the program?

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Business

Kaila

10 April, 08:16

A firm is accustomed to training operators who do certain tasks on a production line. those operators who attend the training course are known to be able to meet their production quotas 90% of the time. new op - erators who do not take the training course only meet their quotas 65% of the time. fifty percent of new op - erators attend the course. given that a new operator meets her production quota, what is the probability that she attended the program?

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Katrina · Answer 1

58%

Given that the new operator met the quota, that means that she's either one of the 90% of the trained operators, or one of the 65% of the untrained operators. And since the split between the trained and untrained operators is 50/50, we have

0.90 * 0.5 = 0.45 of all the operators have been trained and meet quota. 0.65 * 0.5 = 0.325 of all the operators have not been trained and meet quota.

So 0.45 + 0.325 = 0.775 of all operators meet quota.

So the probability of her being trained is

0.45 / 0.775 = 0.580645161 = 58.0645161%

Rounding to 2 significant figures gives 58%