Respuesta :
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 [tex]\times[/tex] Probability that batteries have defects given that it is produced by Factory A
= P(A) [tex]\times[/tex] P(D/A)
= 0.60 [tex]\times[/tex] 0.02 = 0.012 or 1.2%
Therefore, the probability that a battery is both made by Factory A and defective is 1.2%.
