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A company has two machines MI and M2. MI produces 60% of its product and M2 produces 40% of its product. M1 produces 5% defective units and M2 produces 4% defective units. A unit is selected at random from the whole product. A) Find the probability that it is defective. B) What is the probability that it was manufactured by machine M2​

Respuesta :

Step-by-step explanation:

Consider the problem

Let, E 1 and E 2

​  be the respective events of items produced by machine A and B.

And let x be the event that the produced item was found to be defective.

Therefore,

Probability of items produced by machine A,P (E 1)=60%= 53

Probability of items produced by machine B,P (E 2)=40%= 52

And,

Probability that machine A produced defective items, P( E 1 x)=2%= 1002

Probability that machine B produced defective items, P( E 2 x)=1%= 1001

So, the probability that randomly selected items was from machine A is given by P( x E 1)

Now, Apply Bayes' Theorem

P( x E 1)= P(E 1)P( E 1x )+P(E 2)P( E 2x)P(E 1)P( E 1x)= 52× 1001 + 5

3× 1002

53× 100

2= 2+5

6= 11

6

Hence, the required probability of machine A is  

11

6

​

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