Question

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?

Answer 1

58%

Step-by-step explanation:

The find out the operators who were trained and met quota, 0.9* 0.5 = 0.45

Operators who were not trained but met quota, 0.65*0.5 = 0.325

Since fifty percent operators attended the course, so the probability is 50/50 of completing quota.

Now, probability of all the operators who completed quota of production is 0.45 + 0.325 = 0.775

So, the probability that the operator who completed quota of production is 0.45/ 0.775 = 0.58, i.e. 58%

We can say that there is a 58% chance that she attended the course that is why she completed the production quota.

Answer 2

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%