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Harman buys 5 boxes of bulbs

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Harman buys 5 boxes of bulbs

by sanju09 » Fri Jan 24, 2014 11:06 pm
Harman buys 5 boxes of bulbs from a company that acknowledges that 4 out of 100 bulbs produced by it are defective. Each box contains 50 bulbs. Harman randomly selects a box he bought and randomly picks 3 bulbs from this box without replacement. What is the probability that exactly one bulb so chosen is defective?

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by bubbliiiiiiii » Sat Jan 25, 2014 7:47 am
sanju09 wrote:Harman buys 5 boxes of bulbs from a company that acknowledges that 4 out of 100 bulbs produced by it are defective. Each box contains 50 bulbs. Harman randomly selects a box he bought and randomly picks 3 bulbs from this box without replacement. What is the probability that exactly one bulb so chosen is defective?

Made-Up
Premise 1: 4/100 => 4% of bulbs are defective
Premise 2: Harman buys 5 boxes each of 50 bulbs => total no. of bulbs he brought is 250
Premise 3: Total defective bulbs @4% = 10 => each box contains 2 defective bulbs
Premise 4: Total non defective bulbs = 240 => each box contains 48 non defective bulbs
Premise 5: Probability of randomly selecting a box = 1/5

Probability of selecting ONLY one defective bulb in 3 without replacement is

2/50*48/49*47/48 = (1x47)/(25x49)

Probability of selecting ONLY one defective bulb in 3 without replacement in three five boxes is:

1/5 * (1x47)/(25x49)


Is this the right way because GMAT problems usually don't end up in such complex calculations!?
Regards,

Pranay
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by theCodeToGMAT » Mon Jan 27, 2014 7:33 pm
sanju09 wrote:Harman buys 5 boxes of bulbs from a company that acknowledges that 4 out of 100 bulbs produced by it are defective. Each box contains 50 bulbs. Harman randomly selects a box he bought and randomly picks 3 bulbs from this box without replacement. What is the probability that exactly one bulb so chosen is defective?
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Sanjeev, can you please post the answer choices along with the OA :)
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by sanju09 » Sun Feb 02, 2014 12:15 am
bubbliiiiiiii wrote:
sanju09 wrote:Harman buys 5 boxes of bulbs from a company that acknowledges that 4 out of 100 bulbs produced by it are defective. Each box contains 50 bulbs. Harman randomly selects a box he bought and randomly picks 3 bulbs from this box without replacement. What is the probability that exactly one bulb so chosen is defective?

Made-Up
Premise 1: 4/100 => 4% of bulbs are defective
Premise 2: Harman buys 5 boxes each of 50 bulbs => total no. of bulbs he brought is 250
Premise 3: Total defective bulbs @4% = 10 => each box contains 2 defective bulbs
Premise 4: Total non defective bulbs = 240 => each box contains 48 non defective bulbs
Premise 5: Probability of randomly selecting a box = 1/5

Probability of selecting ONLY one defective bulb in 3 without replacement is

2/50*48/49*47/48 = (1x47)/(25x49)

Probability of selecting ONLY one defective bulb in 3 without replacement in three five boxes is:

1/5 * (1x47)/(25x49)


Is this the right way because GMAT problems usually don't end up in such complex calculations!?
If we know that each box is same, then why do we need to consider which box?
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
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by sanju09 » Sun Feb 02, 2014 12:21 am
theCodeToGMAT wrote:
sanju09 wrote:Harman buys 5 boxes of bulbs from a company that acknowledges that 4 out of 100 bulbs produced by it are defective. Each box contains 50 bulbs. Harman randomly selects a box he bought and randomly picks 3 bulbs from this box without replacement. What is the probability that exactly one bulb so chosen is defective?
Made-Up
Sanjeev, can you please post the answer choices along with the OA :)
Sorry for checking it so late, Rahul. The questions that I post on GMAT Math page without answers are the experimental questions whose development is under process. I didn't work on it since long nor I received enough replies to finalize everything. So please wait for the OA and the explanation.
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by bubbliiiiiiii » Sun Feb 02, 2014 8:58 pm
sanju09 wrote:
bubbliiiiiiii wrote:
sanju09 wrote:Harman buys 5 boxes of bulbs from a company that acknowledges that 4 out of 100 bulbs produced by it are defective. Each box contains 50 bulbs. Harman randomly selects a box he bought and randomly picks 3 bulbs from this box without replacement. What is the probability that exactly one bulb so chosen is defective?

Made-Up
Premise 1: 4/100 => 4% of bulbs are defective
Premise 2: Harman buys 5 boxes each of 50 bulbs => total no. of bulbs he brought is 250
Premise 3: Total defective bulbs @4% = 10 => each box contains 2 defective bulbs
Premise 4: Total non defective bulbs = 240 => each box contains 48 non defective bulbs
Premise 5: Probability of randomly selecting a box = 1/5

Probability of selecting ONLY one defective bulb in 3 without replacement is

2/50*48/49*47/48 = (1x47)/(25x49)

Probability of selecting ONLY one defective bulb in 3 without replacement in three five boxes is:

1/5 * (1x47)/(25x49)


Is this the right way because GMAT problems usually don't end up in such complex calculations!?
If we know that each box is same, then why do we need to consider which box?
I did that because because Harman chooses 1 box out of 5 and then selects three bulbs without replacement.?!
Regards,

Pranay
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by vipulgoyal » Sun Feb 02, 2014 10:06 pm
{5c1(one out of 5 box)*2c1(one defective out of 2)*48c2(2 non defective out of 48)*3(order by which they arranged 3!/2!)}/250c3

Please share the OA
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