Quality Motors has three plants. Plant 1 produces 35% of the car output, plant 2 produces 20% and plant 3 produces the remaining 45%. One percent of the output of plant 1 is defective, 1.8% of the output of plant 2 is defective and 2% of the output of plant 3 is defective. The annual total production of Quality Motors is 1,000,000 cars. A car is chosen at random from the annual output and is found defection. Use Bayes' Rule to find the probability that it came from plant 2.

The probability that it came from plant 2 is 0.224.

Step-by-step explanation:

We are given that Quality Motors has three plants. Plant 1 produces 35% of the car output, plant 2 produces 20% and plant 3 produces the remaining 45%.

One percent of the output of plant 1 is defective, 1.8% of the output of plant 2 is defective and 2% of the output of plant 3 is defective.

Let the Probability that car output is produced by Plant 1 = P(A) = 0.35

Probability that car output is produced by Plant 2 = P(A) = 0.20

Probability that car output is produced by Plant 3 = P(A) = 0.45

Also, let D = event that output is defective

So, Probability that output defective given that it was produced by plant 1 = P(D/A) = 0.01

Probability that output defective given that it was produced by plant 2 = P(D/B) = 0.018

Probability that output defective given that it was produced by plant 3 = P(D/C) = 0.02

Now, a car is chosen at random from the annual output and is found defection so, the probability that it came from plant 2 is = P(B/D)

We will use the concept of Bayes' Theorem here to calculate the above probability.

SO,  P(B/D)  =  

                    =  

                    =  

                    =  0.224

Hence, the required probability is 0.224.

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

step-by-step explanation: