Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Three plants manufacture hard drives and ship them to a warehouse for distribution. Plant I produces 54% of the warehouses inventory with a 4% defect rate. Plant II produces 35% of the warehouses inventory with an 8% defect rate. Plant III produces the remainder of the warehouses inventory with a 12% defect rate. (a) (5 points) A warehouse inspector selects one hard drive at random. What is the probability that a randomly selected hard drive is defectiv

Sagot :

abiolataiwo2015

Answer:

A. 0.028

B. 0.0628

C. 0.45

Step-by-step explanation:

A. Calculation to determine the probability that it is adefective hard drive and from plant II

Using CONDITIONAL PROBABILITY formula

P(B∩A2) =P(A2)P(B|A2)

Let plug in the formula

P(B∩A2)= 0.35×0.08

P(B∩A2)= 0.028

Therefore the probability that it is adefective hard drive and from plant II will be 0.028

B. Calculation to determine the probability that a randomly selected hard drive is defective

Using LAW OF TOTAL PROBABILITY formula

P(B) =P(A1)P(B|A1) +P(A2)P(B|A2) +P(A3)P(B|A3)

Let plug in the formula

P(B)= 0.54×0.04 + 0.35×0.08 + 0.11×0.12

P(B)=0.0216+0.028+0.0132

P(B)= 0.0628

Therefore the probability that a randomly selected hard drive is defective is 0.0628

C. Calculation to determine the probability that it came from plant II

Using CONDITIONAL PROBABILITY formula two twice

P(A2|B) =P(A2∩B)/P(B)

Let plug in the formula

P(A2|B)=0.0280/0.0628

P(A2|B)= 0.45

Therefore the probability that it came from plant II is 0.45

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.