Acompany collected information on the number of faulty bulbs manufactured on two different machines. they took 200 randomly selected bulbs from each machine and determined how many bulbs were faulty. they recorded the information in the table given below.

machine m (m) machine n (n) total
faulty (f) 22 36 58
not faulty (nf) 178 164 342
total 200 200 400

using the table above, determine which of the following statements is true if one of the bulbs included in the sample was chosen at random.
a.
the probability that the bulb is not faulty given that it was from machine m is less than the probability that the bulb is from machine m given that it is not faulty.
b.
the probability that the bulb is faulty given that it was from machine n is greater than the probability that the bulb is from machine n given that it is faulty.
c.
the probability that the bulb is not faulty given that it was from machine n is greater than the probability that the bulb is from machine n given that it is not faulty.
d.
the probability that the bulb is faulty given that it was from machine m is greater than the probability that the bulb is from machine n given that it is faulty.
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