Answer:
A. 78%
B. 1.92%
Step-by-step explanation:
Given the information:
- 85% of all batteries produced are good
- The inspector correctly classifies the battery 90%
A. What percentage of the batteries will be “classified as good”?
The percentage of batteries are not good is:
100% - 85% = 15% and of those 100-90 = 10% will be classified as good. Hence, we have:
= 0.85*0.9 + 0.15*0.1 = 0.78
= 78%
So 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?
We will use the conditional probability formula in this situation:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex] where:
- P(A) is the probability of A happening. (A is classified as good) => P(A) = 78%
- P(B|A) is the probability of event B happening, given that A happened. (B classified as detective)
- [tex]P(A \cap B)[/tex] is the probability of both events happening => [tex]P(A \cap B) = 0.15*0.1 = 0.015[/tex] (5% of the batteries are not good. Of those, 100-90 = 10% will be classified as good)
We have:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex] = [tex]\frac{0.015}{0.78}[/tex] = 0.0192 = 1.92%
Hence, 1.92% probability that a battery is defective given that it was classified as good
