Home
Class 12
MATHS
In a bolt factory, there machines A, B, ...

In a bolt factory, there machines A, B, C, manufature 25%,35% and 40% of the total production respectively. Of their respective outputs, 5%, 4% and 2% are defective. A bolt is drawn at random from the total product and it is found to be defective. Find the probability that it was manufactured by the machine C.

Text Solution

AI Generated Solution

To solve the problem, we will use Bayes' theorem. We need to find the probability that a defective bolt was manufactured by machine C, given that the bolt is defective. ### Step-by-Step Solution: 1. **Define Events:** - Let \( E_1 \): the event that the bolt is manufactured by machine A. - Let \( E_2 \): the event that the bolt is manufactured by machine B. - Let \( E_3 \): the event that the bolt is manufactured by machine C. ...
Promotional Banner

Similar Questions

Explore conceptually related problems

. In a bolt factory, machines M M2 M3 manufacture respectively 25, 35 and 40 percent of the total product. Of their output 5, 4 and 2 percent respectively are defective bolts. One bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine M3? 12'3

In a factory which manufactures bolts, machines A.B and C manufacture respectively 25%,35% and 40% 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 it is manufactured by the machine B?

In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25%, 35% and 40% of the factory's total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X?

In a bolt factory machines, A, B and C manufacture bolts in the ratio 6:3:1. 2%, 5% and 10% of the bolts produced by them respectively are defective. A bolt is picked up at random from the product and is found to be defective. What is the probability that it has been manufactured by machine A?

In a bolt factory, machines A,B and C manufacture 25%, 35% and 40% respectively of the total output from which 55, 4% and 2% respectively are defective. A bolt is drawn and is found to be defective. What is the probability that it was manufactured by the machine C?