Answer:
a) 78% of the batteries will be classified as good.
b) 1.92% probability that a battery is defective given that it was classified as good
Step-by-step explanation:
A brief introduction about the conditional probability formula.
Conditional probability formula:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
A.What percentage of the batteries will be“classified as good”?
85% are good, and of those, 90% are classified as good.
15% are not good and of those, 10% are classified as good.
Then
0.9*0.85 + 0.1*0.15 = 0.78
78% of the batteries will be classified as good.
B.What is the probability that a battery is defective given that it was classified as good?
Conditional probability.
A: Classified as good
B: Defective.
From a), P(A) = 0.78
Intersection:
Classified as good, but defective.
This is 10% of 15%.
[tex]P(A \cap B) = 0.1*0.15 = 0.015[/tex]
Then:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.015}{0.78} = 0.0192[/tex]
1.92% probability that a battery is defective given that it was classified as good
