Question

Two shipments of components were received by a factory and stored in two separate bins. Shipment I has4% ofits contents defective, while shipment II has5% of its contents defective. If it is equally likely an employee willgo to either bin and select a component randomly, what is the probability a selected component is defective

Answer 1

0.045 = 4.5% probability a selected component is defective

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

Probability of a defective component:

4% of 50%(shipment I)

5% of 50%(shipment II). So

`p = 0.04*0.5 + 0.05*0.5 = 0.045`

0.045 = 4.5% probability a selected component is defective