Question

You get GPS units from two manufacturers, A and B. You get 43% of your units from A and 57% of your units from B. In the past, 2% of the units from A have been defective, and 1.5% of the units from B have been defective. Assuming this holds true, if a GPS unit is found to be defective what is the probability that it came from manufacturer A (think Bayes Theorem AND round to two decimal places)

Answer 1

0.5015 = 50.15% probability that it came from manufacturer A.

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.

In this question:

Event A: Defective

Event B: From manufacturer A.

Probability a unit is defective:

2% of 43%(from manufacturer A)

1.5% of 57%(from manufacturer B). So

`P(A) = 0.02*0.43 + 0.015*0.57 = 0.01715`

Probability a unit is defective and from manufacturer A:

2% of 43%. So

`P(A \cap B) = 0.02*0.43 = 0.0086`

What is the probability that it came from manufacturer A?

`P(B|A) = (P(A \cap B))/(P(A)) = (0.0086)/(0.01715) = 0.5015`

0.5015 = 50.15% probability that it came from manufacturer A.