Q# Bay’s Theorem: A Construction Company finds that an experienced machine operator of its company (one or more years of experience) will produce a defective item 1.5% of the time. Operators with some experience (up to one year) will produce a 2.5% defective rate and new operators will produce a 5% defective rate. The company has 65% experienced employees, 25% with some experience and 10% new employees. Find the probability that
i.
Experienced operator of a company
produced a particular defective item.
ii. Operator with some experience of a company produced a particular defective item.
iii.
New operator of a company produced a
particular defective item.
let’s create some events to work with.
D: “operator produces
a defective item”
E: “experienced
operator”
S: “operator with some experience”
N: “new operator”
With these definitions, the information in the problem
statement can be written as
P(E) = 0.65
P(D/E) = 0.015
P(S) = 0.25
P(D/S) = 0.025
P(N) = 0.1
P(D/N) = 0.05
The
probability that an experience operator produces a defective item, we are
interested in the event E and D. These probabilities lie
along the top branch so
P(E
and D) = P(D/E) P(E) = (0.015)(0.65)
= 0.0097
=0.97% Answer
To find
the probability that a particular defective item was produced by a Experienced
operator, we need to compute P(E | D). The appropriate form
of Baye’s Theorem is
=
= 0.4642
= 46.42% Answer
To find
the probability that a particular defective item was produced by a Some Experienced
operator, we need to compute P(S | D). The appropriate form
of Baye’s Theorem is
=
= 0.2976
= 29.76% Answer
To find the probability that a particular
defective item was produced by aNew operator, we need to compute P(N | D). The appropriate form
of Baye’s Theorem is
P
=
= 0.2381
= 23.81% Answer
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