A firm trains operators to do certain tasks on a production

A firm trains operators to do certain tasks on a production line. Those operators who attend the training course are know to be able to meet their production quotas 90 percentage of the time. Operators who do not take the training course only meet their quotas 65 percentage of the time. Fifty percent of operators attend the course.

Solution

3.

a)

Let

A = attended
M = meets the quota

Thus,

P(M) = P(A) P(M|A) + P(A\') P(M|A\')

= 0.50*0.90 + 0.50*0.65

= 0.775 [ANSWER]

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b)

P(A|M) = P(A) P(M|A) / P(M)

= 0.50*0.90/0.775

= 0.580645161 [ANSWER]