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 operators who do not take the training course only meet their quotas 65% of the time. Fifty percent of new operators 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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KrystaCort KrystaCort · Answer 1 · 2019-09-25T12:46:08+02:00

Answer:

Probability = 0.58

Step-by-step explanation:

This problem is solve by using Baye's Probability.

Let P(A) = Probability that operator attended training course = 50% = 0.5

P(B) = Probability that operator not attended training course = 50% = 0.5

Also P(Q) = Probability that operator meet their production quotas

Then, P(Q|A) = 90% = 0.9

P(Q|B) = 65% = 0.65

P(A|Q) = ?

Then by Baye's Theorem,

[tex]P(A|Q) = \dfrac{P(Q|A) \times P(A)}{P(Q|A) \times P(A)+P(Q|B) \times P(B)}[/tex]

⇒ [tex]P(A|Q) = \dfrac{0.9 \times\0.5 }{0.9 \times\0.5+0.65 \times\0.5}[/tex]

⇒ P(A|Q) = 0.58

which is required probability.