Two factories — Factory A and Factory B — design batteries to be used in mobile phones. Factory A produces 60% of all batteries,

Question

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Two factories — Factory A and Factory B — design batteries to be used in mobile phones. Factory A produces 60% of all batteries,

and Factory B produces the other 40%. 2% of Factory A's batteries have defects, and 4% of Factory B's batteries have defects. What is the probability that a battery is both made by Factory A and defective? *

Mathematics

1 answer:

tester [12.3K] · Answer 1 · 2026-02-27T00:48:22+03:00

Answer:

The likelihood of a battery being produced by Factory A and being defective is 0.012, which corresponds to 1.2%.

Step-by-step explanation:

We have two manufacturers of batteries for mobile phones: Factory A and Factory B. Factory A is responsible for 60% of the total battery production, while Factory B accounts for the remaining 40%.

Out of the batteries made by Factory A, 2% are found to be defective, whereas 4% of those from Factory B are defective.

Let P(A) denote the probability that a battery comes from Factory A, therefore P(A) = 0.60.

The probability that a battery originates from Factory B can be denoted as P(B) = 0.40.

Furthermore, define D as the event indicating that a battery is defective.

Thus, the probability of a defect given that a battery is from Factory A is P(D/A) = 0.02.

For Factory B, the probability of a defect given it is from there is P(D/B) = 0.04.

The probability for a battery being made at Factory A and also being defective can be calculated as follows:

Probability that Factory A produces batteries $\times$ Probability that a battery from Factory A is defective

= P(A) $\times$ P(D/A)

= 0.60 $\times$ 0.02 = 0.012 or 1.2%

Conclusively, the probability that a battery is both from Factory A and defective is 1.2%.