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A shipment of 500 bulbs contains 10% defective bulbs. If three

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A shipment of 500 bulbs contains 10% defective bulbs. If three  [#permalink]

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New post 16 Mar 2018, 09:51
1
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

39% (02:57) correct 61% (02:57) wrong based on 45 sessions

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A shipment of 500 bulbs contains 10% defective bulbs. If three bulbs are chosen
randomly, what is the probability that exactly 2 of them are defective?

A. \(\frac{1}{500}\)
B. \(\frac{3}{500}\)
C. \(\frac{3}{1000}\)
D. \(\frac{9}{1000}\)
E. \(\frac{27}{1000}\)

Source: Experts Global

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A shipment of 500 bulbs contains 10% defective bulbs. If three  [#permalink]

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New post 16 Mar 2018, 12:15
Since the number of bulb is too big, i have to use approximation to arrive to the conclusion

Probability that exactly 2 bulb will be broken: 50/500 * 49/499 * 448/498 = 0.1 * 0.1 * 0.9 = 0.009

Since 2 broken light bulb can be arrange in 3!/2! way, the final answer will be: 0.09 * 3 = 0.027 => Answer E
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Re: A shipment of 500 bulbs contains 10% defective bulbs. If three  [#permalink]

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New post 18 Mar 2018, 07:45
pushpitkc wrote:
A shipment of 500 bulbs contains 10% defective bulbs. If three bulbs are chosen
randomly, what is the probability that exactly 2 of them are defective?

A. \(\frac{1}{500}\)
B. \(\frac{3}{500}\)
C. \(\frac{3}{1000}\)
D. \(\frac{9}{1000}\)
E. \(\frac{27}{1000}\)

Source: Experts Global


Number of Defective Bulbs = 50
Number of Non-Defective Bulbs = 450
Ways of Selecting Exactly 2 Ddefective Bulbs & 1 non-Defective Bulb
= \(50C2 * 450C1\)
Total Number of Ways = \(500C3.\)

Probability = \(50C2 * 450C1 / 500C3.\) = 0.027
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Re: A shipment of 500 bulbs contains 10% defective bulbs. If three  [#permalink]

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New post 29 Mar 2018, 07:25
ANSWER:E
Probability of bulb being defective: 1/10
Probability of bulb being non- defective: 1-1/10=9/10
No. of ways of choosing 2 Defective and one Non Defective Bulb: 3!/2!=3
Probability required: 3*(1/10)*(1/10)*(9/10)=27/1000
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Re: A shipment of 500 bulbs contains 10% defective bulbs. If three &nbs [#permalink] 29 Mar 2018, 07:25
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