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!?

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

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?

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.

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.?!

{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