Answer:
30.77% probability that this failure is from A.
38.46% probability that this failure is from B.
30.77% probability that this failure is from C.
Step-by-step explanation:
Conditional probability:
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
30% probability of board A being chosen.
Board A has a 4% probability of failure.
30% probability of board B being chosen.
Board B has a 5% probability of failure.
40% probability of board C being chosen.
Board B has a 3% probability of failure.
For all these questions:
Event A: Failure
So
Probability that this failure is from A:
Event B: Board A is chosen.
Intersection:
Failure from board A:
30.77% probability that this failure is from A.
Probability that this failure is from B:
Event B: Board B is chosen.
Intersection:
Failure from board B:
38.46% probability that this failure is from B.
Probability that this failure is from C:
Event B: Board C is chosen.
Intersection:
Failure from board C:
30.77% probability that this failure is from C.