Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

23 Apr 2012, 14:43

11

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

58% (01:45) correct
42% (00:37) wrong based on 308 sessions

HideShow timer Statistics

A string of 10 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?

A. 0.06 B. (0.06)^10 C. 1 - (0.06)^10 D. (0.94)^10 E. 1 - (0.94)^10

I know it's not among the answer choices, but could you please tell me what's wrong with thinking that the result should be 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 = 10*0.06 = 0.6 ?

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

24 Apr 2012, 13:12

10

This post received KUDOS

Expert's post

10

This post was BOOKMARKED

massi2884 wrote:

A string of 10 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?

A. 0.06 B. (0.06)^10 C. 1 - (0.06)^10 D. (0.94)^10 E. 1 - (0.94)^10

I know it's not among the answer choices, but could you please tell me what's wrong with thinking that the result should be 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 = 10*0.06 = 0.6 ?

The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.

The opposite event is when none of the 10 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the the probability that none of the 10 light bulbs fails is 0.94^10.

Hence, the probability that at least one light bulb fails is 1-0.94^10.

Answer: E.

Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 10, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6, which is not possible since the probability of an event cannot be more than 1 (100%).

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

23 Apr 2012, 21:37

9

This post received KUDOS

1

This post was BOOKMARKED

Quote:

I know it's not among the answer choices, but could you please tell me what's wrong with thinking that the result should be 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 = 10*0.06 = 0.6 ?

It only takes one failure in any of the 10 slots to create the failure. For example if the second bulb fails, the whole string fails. If the 9th bulb fails, the string will fail too. Therefore the one and only chance for the strings to stay lit would be 10 consecutive non-failures.

(.94)^10 = a lit string. Now it becomes 1-(.94)^10 since you're looking for the probability that the string of lights will fail.

Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink]

Show Tags

16 May 2012, 03:47

3

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

Merging similar topics.

alexpavlos wrote:

A string of 10 lightbulbs is wired in such a way that if any individal lightbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during the period T is 0.06, what is the probability that the string of lightbulbs will fail during the period T?

A) 0.06 B) (0.06)^10 C) 1 - (0.06)^10 D) (0.94)^10 E) 1 - (0.94)^10

I still believe it is B. Why exactly is it E? I understand that E is 1- the probability of NOT failing. But I would assume the B is just the probability of it failing.

We are told that the string of light bulbs will fail if at least one light bulb fails. (0.06)^10 is the probability that all 10 lightbulbs will fail.

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

12 May 2015, 02:41

2

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

Ergenekon wrote:

Bunuel wrote:

Dmba wrote:

Can please someone explain why answer A is wrong? We are told that the entire wire will fail if one bulb fails. Since the probability of one bulb to fail is 0.6 then the probability of the entire wire to fail should be also 0.6.

We are told that the string of light bulbs will fail if at least one light bulb fails. So, the favorable outcome is NOT one bulb to fail but the sum of the probabilities that one, two, three, ... or all 10 to fail OR which is the same, 1 minus the probability that neither fails.

Bunuel, can you solve this question with alternative method that you mentioned above -- the favorable outcome is NOT one bulb to fail but the sum of the probabilities that one, two, three, ... or all 10 to fail OR which is the same, [i]1 minus the probability that neither fails

The important point here is to select the bulbs which would fail out of the total bulbs for each case. So, when we write the probability equation for 1 bulb failing, there can be 10 ways in which a bulb can fail.

Similarly, when you write the probability equation for the non-event method i.e.

Both the probability equations will give you the same result. However you would notice that the non-event method is far more easier to calculate and comprehend than the event method.

For a probability question it is recommended to evaluate the number of cases in the event and the non-event method before proceeding with the solution.

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

17 Jan 2013, 02:20

1

This post received KUDOS

thangvietnam wrote:

I understand why E is correct

but not understand why the result can not be 0.6. pls, explain using reasoning not using the quatitative.

why we can not add all possibilities?

SUGGESTED REASON: Since P(A or B) = P(A) + P(B) – P(AnB)....if 2 events can happen at the same time P(AnB) is not 0 There exists a probability that 2 or more lightbulbs can fail at the same time P(A or B or C) = P(A) + P(B) + P(C) – 2P(AnBnC) – [sum of exactly 2 groups members]

So for 10 items, P(A or B or...or J) = P(A) + P(B)+...P(J) -...LOONG & COMPLEX calculations

I hope my reasoning is correct? _________________

KUDOS me if you feel my contribution has helped you.

A string of 10 lightbulbs is wired in such a way that if any [#permalink]

Show Tags

16 May 2012, 03:41

A string of 10 lightbulbs is wired in such a way that if any individal lightbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during the period T is 0.06, what is the probability that the string of lightbulbs will fail during the period T?

A) 0.06 B) (0.06)^10 C) 1 - (0.06)^10 D) (0.94)^10 E) 1 - (0.94)^10

I still believe it is B. Why exactly is it E? I understand that E is 1- the probability of NOT failing. But I would assume the B is just the probability of it failing.

Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink]

Show Tags

16 May 2012, 04:45

Bunuel wrote:

Merging similar topics.

alexpavlos wrote:

A string of 10 lightbulbs is wired in such a way that if any individal lightbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during the period T is 0.06, what is the probability that the string of lightbulbs will fail during the period T?

A) 0.06 B) (0.06)^10 C) 1 - (0.06)^10 D) (0.94)^10 E) 1 - (0.94)^10

I still believe it is B. Why exactly is it E? I understand that E is 1- the probability of NOT failing. But I would assume the B is just the probability of it failing.

We are told that the string of light bulbs will fail if at least one light bulb fails. (0.06)^10 is the probability that all 10 lightbulbs will fail.

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

16 Jan 2014, 23:28

massi2884 wrote:

A string of 10 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?

A. 0.06 B. (0.06)^10 C. 1 - (0.06)^10 D. (0.94)^10 E. 1 - (0.94)^10

I know it's not among the answer choices, but could you please tell me what's wrong with thinking that the result should be 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 = 10*0.06 = 0.6 ?

Probability of Failing = 1 - probability of success Probability of failing = 1 - (1 - 0.06)^10 = 1 - (0.94)^10

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

17 Jan 2014, 06:37

Can please someone explain why answer A is wrong? We are told that the entire wire will fail if one bulb fails. Since the probability of one bulb to fail is 0.6 then the probability of the entire wire to fail should be also 0.6.

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

17 Jan 2014, 06:46

Expert's post

Dmba wrote:

Can please someone explain why answer A is wrong? We are told that the entire wire will fail if one bulb fails. Since the probability of one bulb to fail is 0.6 then the probability of the entire wire to fail should be also 0.6.

We are told that the string of light bulbs will fail if at least one light bulb fails. So, the favorable outcome is NOT one bulb to fail but the sum of the probabilities that one, two, three, ... or all 10 to fail OR which is the same, 1 minus the probability that neither fails.

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

31 Jan 2015, 22:30

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

12 May 2015, 00:41

Bunuel wrote:

Dmba wrote:

Can please someone explain why answer A is wrong? We are told that the entire wire will fail if one bulb fails. Since the probability of one bulb to fail is 0.6 then the probability of the entire wire to fail should be also 0.6.

We are told that the string of light bulbs will fail if at least one light bulb fails. So, the favorable outcome is NOT one bulb to fail but the sum of the probabilities that one, two, three, ... or all 10 to fail OR which is the same, 1 minus the probability that neither fails.

Bunuel, can you solve this question with alternative method that you mentioned above -- the favorable outcome is NOT one bulb to fail but the sum of the probabilities that one, two, three, ... or all 10 to fail OR which is the same, [i]1 minus the probability that neither fails

Did not give the same result. _________________

If my post was helpful, press Kudos. If not, then just press Kudos !!!

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

15 May 2016, 07:48

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: A string of 10 light bulbs is wired in such a way that if [#permalink]

Show Tags

15 May 2016, 08:41

massi2884 wrote:

A string of 10 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?

A. 0.06 B. (0.06)^10 C. 1 - (0.06)^10 D. (0.94)^10 E. 1 - (0.94)^10

Probability of NOT failing one light bulb = 1-.06= 0.94 Probability of NOT failing all light bulbs = 0.94^10

Probability of failing= 1-0.94^10

E is the answer _________________

I welcome critical analysis of my post!! That will help me reach 700+

gmatclubot

Re: A string of 10 light bulbs is wired in such a way that if
[#permalink]
15 May 2016, 08:41

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...