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Tatiana [17]
2 years ago
10

1. A company produces batteries. On average, 85% of all batteries produced are good. Each battery is tested before being dispatc

hed, and the inspector correctly classifies the battery 90% of the time.
A. What percentage 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?
(3+3=6 marks)
Mathematics
1 answer:
pogonyaev2 years ago
7 0

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:

P(B|A) = \frac{P(A \cap B)}{P(A)} 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)
  • P(A \cap B) is the probability of both events happening => P(A \cap B) = 0.15*0.1 = 0.015 (5% of the batteries are not good. Of those, 100-90 = 10% will be classified as good)

We have:

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.015}{0.78} = 0.0192 = 1.92%

Hence, 1.92% probability that a battery is defective given that it was classified as good

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