Two production lines are used to pack sugar into 5 kg bags. Line 1 produces twice as many bags as does line 2. One percent of the bags from line 1 are defective in that they fail to meet a purity specification, while 3% of the bags from line 2 are defective. A bag is randomly chosen for inspection.

a. What is the probability that it came from line 1?

b. What is the probability that it is defective?

c. If the bag is defective, what is the probability that it came from line 1?

d. If the bag is not defective, what is the probability that it came from line 1?

Step 1 of 5:

Given that there are two lines,line1 and line2 used to pack sugar into bags of 5kg.

Line1 produces bags equal to twice the number of bags produced by line2.

1% of bags from line1 are fail to meet the purity specification and hence are considered as defectives.

3% of bags from line2 are fail to meet the purity specification and hence are considered as defectives.

A bag from the lot is randomly chosen for inspection.

Using all these data we have to find out the required probabilities.

Step 2 of 5:

(a)

Here we have to find the probability that the randomly chosen bag is from line1.

Let x denotes the number of bags produced by line2.

Then,the total number of bags produced by line1 is equal to 2x,and total number of bags produced by line1 and line2 is equal to x+2x.

Thus,

P(Chosen bag came from line1)=

=

=

=0.6667

Hence,the probability that randomly chosen bag came from line 1 is 0.667.

Step 3 of 5:

(b)

Here we have to find the probability that the randomly chosen bag is defective.

It is given by,

P(Chosen bag is defective)=P(chosen bag is from line 1)*P(defective bags in line1)+P(chosen bag is from line 2)*P(defective bags in line 2)

=*+*

=*0.01+*0.03

=*0.01+*0.03

=0.6667*0.01+0.3333*0.03

=0.006667+0.009999

=0.016666

Thus,the probability that the randomly chosen bag is defective is 0.01666.