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In a toy manufacturing company the probability that the toy manufact
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17 Nov 2024, 15:23
17 Nov 2024, 15:23
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In a toy manufacturing company the probability that the toy manufactured is defective is 0.1. For shipment purposes 5 toys are packed in a box. The shipment of the box of toys is only done if the inspection department of the company clears the box of toys after inspection. Due to strict government regulatory guidelines the inspection department of the company rejects the box of toys for shipment even if one of the toys is defective. What is the probability that the box of toys will be not be cleared for shipment by the inspection department of the toy manufacturing company?
A. \(0.1\)
B. \(0.15\)
C. \(1 – (0.1)^5\)
D. \(1 – (0.9)^5\)
E. \(1\)
A. \(0.1\)
B. \(0.15\)
C. \(1 – (0.1)^5\)
D. \(1 – (0.9)^5\)
E. \(1\)
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Re: In a toy manufacturing company the probability that the toy manufact
[#permalink]
21 Dec 2024, 13:03
21 Dec 2024, 13:03
Expert Reply
As the probability of the toy manufactured being defective is 0.1 , the probability of the toy being good would be $\(1-0.1=0.9(\because \mathrm{P}($ An event will happen $)+\mathrm{P}($ Event won't happen $)=1)\)$
We know that the shipment of the 5 boxes of toys gets rejected even if there is one toy found defective, so the probability of the rejection of the shipment is same as probability of finding at least one of the five toy boxes defective.
As the Probability \((At least 1 ) = 1 - Probability (None)\), we get Probability (At least one of the toys is defective) $\(=1 - \)$ \(Probability (None of the 5 boxes is defective) $=1-(0.9)^5\)$.
Hence the answer is (D).
We know that the shipment of the 5 boxes of toys gets rejected even if there is one toy found defective, so the probability of the rejection of the shipment is same as probability of finding at least one of the five toy boxes defective.
As the Probability \((At least 1 ) = 1 - Probability (None)\), we get Probability (At least one of the toys is defective) $\(=1 - \)$ \(Probability (None of the 5 boxes is defective) $=1-(0.9)^5\)$.
Hence the answer is (D).
gmatclubot
Re: In a toy manufacturing company the probability that the toy manufact [#permalink]
21 Dec 2024, 13:03
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