# Three machi

Given:

Machine E1 produces 50% of the total output.

Machine E2 produces 25% of the total output.

Machine E3 produces 25% of the total output.

4% of the tubes produced by machine E1 are defective.

4% of the tubes produced by machine E2 are defective.

5% of the tubes produced by machine E3 are defective.

There are three mutually exclusive ways to pick up a defective tube produced by one of the three machines –

a. Tube was produced by machine E1, and then, the tube is defective

b. Tube was produced by machine E2, and then, the tube is defective

c. Tube was produced by machine E3, and then, the tube is defective

Let X1 be the event that the tube is produced by machine E1, X2 be the event that the tube is produced by machine E2 and X3 be the event that the tube is produced by machine E3.

As 50% of the total output is produced by machine E1, we have

Similarly, as each of machines E2 and E3 produces 25% of the total tubes, we have

Let X4 denote the event that the tube is defective.

Hence, we have

4% of the tubes produced by machine E1 are defective.

Similarly,

We also have

5% of the tubes produced by machine E3 are defective.

Using the theorem of total probability, we get

P(X4) = P(X1)P(X4|X1) + P(X2)P(X4|X2) + P(X3)P(X4|X3)

Thus, the probability of the tube being defective is.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

A bag A contains RD Sharma - Volume 2

The contents of tRD Sharma - Volume 2

A girl throws a dMathematics - Board Papers

Three urns contaiRD Sharma - Volume 2

Two groups are coMathematics - Board Papers

The contents of tRD Sharma - Volume 2

Suppose a girl thMathematics - Board Papers

There are three cMathematics - Board Papers

Given three identMathematics - Board Papers