Two factories produce identical clocks. The production of the first factory consists of 10,000 clocks of which 100 are defective. The second factory produces 20,000 clocks of which 300 are defective. What is the probability that a particular defective clock was produced in the first factory ?
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Given:
Clocks in first factory = 10,000
Defective = 100
Clocks in second factory = 20,000
Defective = 300
To Find:
Probability a defective clock was produced in the first factory
Solution:
Let the defective clock be = A
Let event of selection of first factory = b1
Let event of selection of second factory = b2
As factories have same occurrence probability thus -
Pb1 = Pb2 = 1/2
Probability of selecting defective clock from first factory -
= 100/10,000
= 1/100
Similarly, from second factory -
= 300/20,000
= 3/200
Thus, total probability -
P(b1/A) = Pb1 x P(A/b1) / Pb1 x P(A/b1) + Pb2 x P(A/b2)
= 1/2 x 1/100 / (1/2 x 1/100) + ( 1/2 x 3/200)
= 2/5
= 0.4
Answer: The probability is 0.4
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