Answer:
P(Bag is Defective) = 0.0167
Step-by-step explanation:
Line 1 produces twice as many bags as line 2. Let x be the number of bags produced by line 2.
No. of bags produced by line 2 = x
No. of bags produced by line 1 = 2x
Probability that the bag has been produced by line 1 can be written as:
P(Line 1) = No. of bags produced by line 1/Total no. of bags
= 2x/(x+2x)
= 2x/3x
P(Line 1) = 2/3. Similarly,
P(Line 2) = x/3x
P(Line 2) = 1/3
1% bags produced by line 1 are defective so the probability of line 1 producing a defective bag is:
P(Defective|Line 1) = 0.01
3% of bags from line 2 are defective, so:
P(Defective|Line 2) = 0.03
b. The probability that the chosen bag is defective can be calculated through the conditional probability formula:
P(A|B) = P(A∩B)/P(B)
<u>P(A∩B) = P(A|B)*P(B)</u>
The chosen defective bag can be either from line 1 or from line 2. So, the probability that the chosen bag is defective is:
P(Bag is Defective) = P(Defective and from Line 1) + P(Defective and from Line 2)
= P(D∩Line 1) + P(D∩Line 2)
= P(Defective|Line 1)*P(Line 1) + P(Defective|Line 2)*P(Line 2)
= (0.01)*(2/3) + (0.03)(1/3)
P(Bag is Defective) = 0.0167
