Two different factories both produce a certain automobile part. The probabbility
ID: 2903354 • Letter: T
Question
Two different factories both produce a certain automobile part. The probabbility that a component from the first factory is defective is 2%, and the probability that a component from the second factory is defective is 5%. In a supply of 180 of the parts, 100 were obtained from the first factory and 80 from the second factory.
a) What is the probability that a part chosen at random from the 180 is from the first factory?
b) What is the probability that a part chosen at random from the 180 is from the second factory?
c) What is the probability that a part chosen at random from the 180 is defective?
d) If the chosen part is defective, what is the probability that it came from the first factory?
Explanation / Answer
Total automobile parts(T) = 180
Automobile parts from first factory (F)= 100
Automobile parts from second factory (S)= 80
The probability that a component from the first factory is defective is 2%,
therefore 2% of 100 parts chosen from first factory are defective
Defective parts from first factory (D1)=(2/100)*100 = 2
and the probability that a component from the second factory is defective is 5%
therefore 5% of 80 parts chosen from second factory are defective
Defective parts from second factory (D2)=(5/100)*80 = 4
Total defective parts from first and second factory
D =D1+D2
D=2+4 =6
a) What is the probability that a part chosen at random from the 180 is from the first factory?
total number of ways to choose a part from 180 parts=180
total number of ways that a part choosen is from first factory =100
therefore,
the probability that a part chosen at random from the 180 is from the first factory =100/180
b) What is the probability that a part chosen at random from the 180 is from the second factory?
total number of ways to choose a part from 180 parts=180
total number of ways that a part choosen is from second factory =80
therefore,
the probability that a part chosen at random from the 180 is from the second factory =80/180
c) What is the probability that a part chosen at random from the 180 is defective?
total number of ways to choose a part from 180 parts=180
total number of ways that a part choosen is defective =D =6
therefore,
the probability that a part chosen at random from the 180 is defective =6/180
d) If the chosen part is defective, what is the probability that it came from the first factory?
total number of ways to choose a defective part = 6
total number of ways that the defective part is from first factory =D1 =2
therefore,
the probability that the defective part came from the first factory =2/6
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