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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8029
GMAT 1: 760 Q51 V42 GPA: 3.82
In a certain factory, the production line which produces the bags has  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 67% (01:07) correct 33% (01:33) wrong based on 98 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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Re: In a certain factory, the production line which produces the bags has  [#permalink]

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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
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Re: In a certain factory, the production line which produces the bags has  [#permalink]

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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) $$1-(0.98)^6$$
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Re: In a certain factory, the production line which produces the bags has  [#permalink]

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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

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8029
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: In a certain factory, the production line which produces the bags has  [#permalink]

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==> 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.
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GMAT 1: 650 Q46 V34 GMAT 2: 620 Q45 V30 GMAT 3: 700 Q45 V40 Re: In a certain factory, the production line which produces the bags has  [#permalink]

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