Please include working out , having trouble with this question thanks A manufact

Question

Please include working out , having trouble with this question thanks

A manufacturing company has three lines producing flirps. Line 1 manufactures 45% of the flirps, line 2 manufactures 35% and line 3 manufactures 20%. However, some flirps produced are faulty. 3% produced in line 1, 1% in line 2 and 0.05% in line 3 are defective. Before being transported to retail outlets, the flirps are sealed into packets of 12 and sent to a central storage depot. A customer received a packet produced in March, which contained 1 defective flirp. What is the probability that this packet was manufactured on production line 1? What is the probability that this packet was manufactured on production line 1?

Explanation / Answer

here we have given

P(line1)=0.45,P(line2)=0.35,P(line3)=0.2

P(faulty|line1)=0.03,P(faulty|line2)=0.01, P(faulty|line3)=0.005

we want to get P(line1/faulty)=P(line1)*P(faulty|line1)=0.45*0.03=0.0135

so required probability of defective flirp was manufactured on production line is=0.0135

we want

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