A factory has 3 machines X, Y and Z producing 1000, 2000 and 3000 bolts per day respectively. The machine X produces 1% defective bolt, Y produces 1.5% and Z produces 2% defective bolts. At the end of a day, a bolt is drawn at random and is found defective. What is the probability that this defective bolt has been produced by the machine X?

A factory has two machines X and Y .X produces 70% and Y produces 30% of the items of which items produced by X have 5% defective items and items produced by Y have 8% defective. An item is drawn at random for the product and is found to be defective. Find the probability that it was produced by Machine Y.

In a factory which manufactures bulbs, machines X, Y and Z manufactures respectively 25%, 35% and 40% of the bulbs. Of their outputs 1, 2 and 3 percent re respectively defective bulbs. A bulb is drawn at random and is found to be defective. What is the probability that it is manufactured by the machine Y?

In a factory which manufactures bolts, machine A, B and C manufacture respectively 25%, 35% and 45% of the bolts. Of their outputs 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that if is manufactured by machine B?

A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% ol the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B:

A factory has two machines A and B. Machine A produces 40% of items of the output and Machine B produces 60% of the items. Further 4% of items produced by Machine A are defective and 5% produced by Machine B are defective. An item is drawn at random. If the drawn item is defective, find the probability that it was produced by Machine B.

A factory has two machines and Il Machine produces 40% of items of the output and Machine Il produces 60% of the items. Further 4% of items produced by Machine are defective and 5% produced by Machine Il are defective. An item is drawn at random. If the drawn item is defective, find the probability that it was produced by Machine II. (See the previous example, compare the questions)

Assume that a factory has two machines. Past records show that machine I produces 20% of the output and machine II produces 80% of the item. Further, 6% of the items produced by machine I were defective and only 1% produced by machine II was defective. If a defective is drawn at random, what is the probability that it was produced by (i) machine I (i) machine II?