The probability an item produced on an assembly line is not tested is 0.85. The

Question

The probability an item produced on an assembly line is not tested is 0.85. The probability an item produced on an assembly line is discarded as a defect is 0.02. Assume an item discarded as defect is mutually exclusive of the item not being tested.

1- What is the probability the item is discarded as a defect given the item is not tested?

2- What is the probability the item is not tested given the item was discarded as a defect?

3- What is the probability the item was not tested or discarded as a defect?

4- What is the probability the item was not tested and discarded as a defect ?

Explanation / Answer

P(Not tested) = 0.85

P(Discarded) = 0.02

P(Not being tested and discarded) = 0 [Because these two are mutually exclusive]

Hence,

1. P(Discarded | Not tested)

= P(Discarded and Not tested) / P(Not tested)

= 0

2. P(Not tested | Discarded) = 0 [By the similar logic as problem 1]

3. P(Not tested or discarded) = P(Not tested) + P(Discarded) = 0.85 + 0.02 = 0.87

4. P(Not tested and discarded) = 0

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