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:
For question b, the conditional probability formula will be used.
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 "classified as good"?
85% of the batteries are good. The inspector correctly classifies the battery 90% of the time, which means that of those 90% will be classified as good.
100-85 = 15% of the batteries are not good. Of those, 100-90 = 10% will be classified as good. Then
0.85*0.9 + 0.15*0.1 = 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?
Event A: classified as good.
Event B: Defective
From A, P(A) = 0.78
Intersection:
100-85 = 15% of the batteries are not good. Of those, 100-90 = 10% will be classified as good.
This means that [tex]P(A \cap B) = 0.15*0.1 = 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
