Question

A company has two plants to manufactur motorbikes. Plant i manufactures 80% motor bikes, and plan ii manufactures 20%. At plant i 85 out of 100 motor bikes are rated standard quality or better. At plant ii only 65 out of 100 motor bike are rated better. I) what is the probability that the motorbike, selected at random come from plant i. If it is known that the motorbike is a standard quality.

Answer 1

Answer:

Step-by-step explanation:

Given  

A company has two plants to manufactur motorbikes. Plant i manufactures 80% motor bikes, and plan ii manufactures 20%. At plant i 85 out of 100.

Let A be the scooter manufactured from plant 1 and B be the scooter manufactured from plant II. Let R be the scooters having better standard quality rate. So we have

P(A) = 8/10, P(B) = 2/10

P(R/A) = 85/100

P(R/B) = 65/100

Now P(A x R) = 0.85 x 0.8 = 0.68

P(B x R) = 0.65 x 0.2 = 0.13

Now P(A∩ R) = 0.68

P(A/R) = 0.8395

P(R) = 0.68 / 0.8395 = 0.81

Now P(B ∩ R) = 0.13

P(B/R) = 0.1605

So P® = 0.13 / 0.1605 = 0.81

Now probability of scooter of standard quality of plant I is 0.8395 and probability of scooter of standard quality of plant II is 0.1605