Question

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? *

Answer 1

Answer:

Probability that a battery is both made by Factory A and defective is 0.012 or 1.2%.

Step-by-step explanation:

We are given that 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.

Let the Probability that factory A produces batteries = P(A) = 0.60

Probability that factory B produces batteries = P(B) = 0.40

Also, let D = event that battery is defective

Probability that batteries have defects given that it is produced by Factory A = P(D/A) = 0.02

Probability that batteries have defects given that it is produced by Factory B = P(D/B) = 0.04

Now, probability that a battery is both made by Factory A and defective = Probability that factory A produces batteries $\times$ Probability that batteries have defects given that it is produced by Factory A

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

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

Therefore, the probability that a battery is both made by Factory A and defective is 1.2%.