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# In a certain factory, the production line which produces the bags has

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 800 Q59 V59
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In a certain factory, the production line which produces the bags has [#permalink]

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05 Jan 2017, 05:51
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Difficulty:

35% (medium)

Question Stats:

67% (00:50) correct 33% (01:17) wrong based on 83 sessions

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In a certain factory, the production line which produces the bags has the probability that a bag selected at random is defective is 0.02. If 6 bags are selected at random, what is the probability that at least one bag is defective?

A. $$0.02^6$$

B. $$(0.02)(0.98)^6$$

C. $$1-(0.02)^6$$

D. $$0.98^6$$

E. $$1-(0.98)^6$$

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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 24 Oct 2016 Posts: 296 Location: India Concentration: Finance, International Business Schools: IIMB GMAT 1: 550 Q42 V28 GPA: 3.96 WE: Human Resources (Retail Banking) Re: In a certain factory, the production line which produces the bags has [#permalink] ### Show Tags 05 Jan 2017, 09:01 the probability of not getting A DEFECTIVE BAG is .98 so probability of getting defective bag equal to 1-(.98)^6 so answer is E Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 3452 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: In a certain factory, the production line which produces the bags has [#permalink] ### Show Tags 05 Jan 2017, 09:28 MathRevolution wrote: In a certain factory, the production line which produces the bags has the probability that a bag selected at random is defective is 0.02. If 6 bags are selected at random, what is the probability that at least one bag is defective? A. $$0.02^6$$ B. $$(0.02)(0.98)^6$$ C. $$1-(0.02)^6$$ D. $$0.98^6$$ E. $$1-(0.98)^6$$ p(d) = 0.02 p(g) = 0.98 Probability of getting 1 defective = 1 - Probability of selecting all good bags. Probability of getting 1 defective = $$1 - P(g)^6$$ Probability of getting 1 defective = $$1 - (0.98)^6$$ Hence, the answer will be (E) $$1-(0.98)^6$$ _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 2611 Location: United States (CA) Re: In a certain factory, the production line which produces the bags has [#permalink] ### Show Tags 06 Jan 2017, 11:07 Expert's post 1 This post was BOOKMARKED MathRevolution wrote: In a certain factory, the production line which produces the bags has the probability that a bag selected at random is defective is 0.02. If 6 bags are selected at random, what is the probability that at least one bag is defective? A. $$0.02^6$$ B. $$(0.02)(0.98)^6$$ C. $$1-(0.02)^6$$ D. $$0.98^6$$ E. $$1-(0.98)^6$$ We are given that the probability that a selected bag is defective is 0.02, so we can determine that the probability of a non-defective bag is 1 - 0.02 = 0.98. We need to determine the probability that when 6 bags are selected at least one bag is defective. We know the following: 1 = P(at least one defective bag is selected) + P(no defective bags are selected) Thus, P(at least one defective bag is selected) = 1 - P(no defective bags are selected) Therefore, we need to determine P(no defective bags are among the 6 selected bags). P(no defective bags are among the 6 selected bags) = 0.98^6 Thus, P(at least one defective bag is among the 6 selected bags) = 1 - 0.98^6 Answer: E _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5437 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: In a certain factory, the production line which produces the bags has [#permalink] ### Show Tags 08 Jan 2017, 18:11 ==> probability that at least one bag is defective=1-probability that all bags are not defective=$$1-(1-0.02)^6$$. Hence, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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Re: In a certain factory, the production line which produces the bags has [#permalink]

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13 Jan 2017, 20:56
Probability of at least one bag is defective = 1 - P(0 defects)
P(a bag is defective) = 0.02
P(a bag is not defective) = 1-0.02 = 0.98

P(at least one bag is defective from a random selection of 6 bags) =1- 0C6*((0.02)^0)*((0.98)^6)
= 1-(0.98)^6
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Re: In a certain factory, the production line which produces the bags has [#permalink]

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28 Jan 2018, 12:44
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Re: In a certain factory, the production line which produces the bags has   [#permalink] 28 Jan 2018, 12:44
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