Q5 120pts) A product comes from one of the four production lines B, B,Bs.Bs with

Question

Q5 120pts) A product comes from one of the four production lines B, B,Bs.Bs with prob- ability 0.4, 0.3, 0.2, 0.1, respectively. The four production lines have defective rate 0.05, 0.03, 0.1, 0.2, respectively. Randomly select a product. (a) [6pts) What is the probability that it is defective? (b) 7pts] Given that the selected product is defective, what is the conditional proba- bility that it comes from production line Bi. (c) (6pts] What is the probability that it comes from B, and is NOT defective?

Explanation / Answer

Given that there are four production lines as B1,B2, B3 and B4.

And let D be the defective

Given that,

P(B1) = 0.4

P(B2) = 0.3

P(B3) = 0.2

P(B4) = 0.1

Also given that,

P(D/B1) = 0.05

P(D/B2) = 0.03

P(D/B3) = 0.1

P(D/B4) = 0.2

a) Now we have to find probability that it is defective.

P(D) = P(D/B1)*P(B1) + P(D/B2)*P(B2) + P(D/B3)*P(B3) + P(D/B4)*P(B4)

= (0.05*0.4) + (0.03*0.3) + (0.1*0.2) +(0.2*0.1)

= 0.069

P(Not defective) = 1 - 0.069 = 0.931

b) Here we have to find P(B1/D).

P(B1/D) = P(D/B1)*P(B1) / P(D)

= (0.05*0.4)/ 0.069

= 0.2899

c) P(B1/ND) = 1 - 0.2899 = 0.7101

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