The Breaker's Manufacturing Company makes 80% of a particular sensor, the Cartin Company makes 15% of them, and the Flutes Company makes the other 5%. The sensors made by Breaker's have a 4% defect rate, the Cartin sensors have a 6% defect rate, and the Flutes sensors have a 9% defect rate. If a sensor is randomly selected from the general population of all sensors, what is the probability that it is defective, given that it was made by Breaker’s?
A.
0.04
B.
0.05
C.
0.15
D.
0.80
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Answers
Given : The Breaker's Manufacturing Company makes 80% of a particular sensor,
the Cartin Company makes 15% of them,
the Flutes Company makes the other 5%.
The sensors made by Breaker's have a 4% defect rate,
the Cartin sensors have a 6% defect rate,
and the Flutes sensors have a 9% defect rate.
a sensor is randomly selected from the general population of all sensors,
To Find : the probability that it is defective, given that it was made by Breaker’s
Solution:
Assume that total sensors made = 1000
Breaker's makes = (80/100) 1000 = 800
Cartin Company makes = (15/100) 1000 = 150
Flutes Company makes = (5/100) 1000 = 50
The sensors made by Breaker's have a 4% defect rate, = (4/100) 800 = 32
the Cartin sensors have a 6% defect rate, = (6/100) 150 = 9
and the Flutes sensors have a 9% defect rate. = (9/100)50 = 4.5
probability that it is defective, given that it was made by Breaker’s
= 32/800
= 0.04
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