GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 19:36

### GMAT Club Daily Prep

#### 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

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

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 Aug 2015
Posts: 2
A string of 10 lightbulbs is wired in such a way that if any  [#permalink]

### Show Tags

06 Aug 2015, 13:04
4
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:09) correct 32% (01:38) wrong based on 151 sessions

### HideShow timer Statistics

A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period?
a. 0.05
b. (0.05)^10
c. 1 - (0.05)^10
d. (0.95)^10
e. 1 - (0.95)^10
CEO
Joined: 20 Mar 2014
Posts: 2595
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: A string of 10 lightbulbs is wired in such a way that if any  [#permalink]

### Show Tags

06 Aug 2015, 13:12
2
1
tonytran14896 wrote:
A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period?
a. 0.05
b. (0.05)^10
c. 1 - (0.05)^10
d. (0.95)^10
e. 1 - (0.95)^10

Probability of a 'fail' = P(F) = 0.05 --> Probability of 'no fail' = 1-P(F) = 1-0.05 = 0.95

Thus, the probability of 10 bulbs to not fail = 0.95*0.95*0.95*0.95*0.95*0.95*0.95*0.95*0.95*0.95 = 0.95^10, D is the correct answer.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: A string of 10 lightbulbs is wired in such a way that if any  [#permalink]

### Show Tags

07 Aug 2015, 00:48
1
tonytran14896 wrote:
A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period?
a. 0.05
b. (0.05)^10
c. 1 - (0.05)^10
d. (0.95)^10
e. 1 - (0.95)^10

Think about it: When will the string of lightbulbs not fail? Only when all lightbulbs stay alive simultaneously.

P (a lightbulb will stay alive) = 1 - 0.05 = 0.95

So probability that all lightbulbs stay live simultaneously $$= 0.95 * 0.95 * 0.95.....0.95 = (0.95)^{10}$$
(0.95s will be multiplied because it is an "and" situation. You need the first "and" the second "and" the third etc to stay alive)

_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 02 Sep 2014
Posts: 6
Location: United States
Concentration: Strategy, Technology
GMAT Date: 08-22-2015
GPA: 3.1
WE: Consulting (Consulting)
A string of 10 lightbulbs is wired in such a way that if any  [#permalink]

### Show Tags

16 Aug 2015, 03:04
VeritasPrepKarishma wrote:
tonytran14896 wrote:
A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period?
a. 0.05
b. (0.05)^10
c. 1 - (0.05)^10
d. (0.95)^10
e. 1 - (0.95)^10

Think about it: When will the string of lightbulbs not fail? Only when all lightbulbs stay alive simultaneously.

P (a lightbulb will stay alive) = 1 - 0.05 = 0.95

So probability that all lightbulbs stay live simultaneously $$= 0.95 * 0.95 * 0.95.....0.95 = (0.95)^{10}$$
(0.95s will be multiplied because it is an "and" situation. You need the first "and" the second "and" the third etc to stay alive)

asking this out of curiosity .what will be the question if the answer would be c .
my thinking is a bit weird please forgive me.
Math Expert
Joined: 02 Sep 2009
Posts: 58427
Re: A string of 10 lightbulbs is wired in such a way that if any  [#permalink]

### Show Tags

16 Aug 2015, 12:35
tonytran14896 wrote:
A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period?
a. 0.05
b. (0.05)^10
c. 1 - (0.05)^10
d. (0.95)^10
e. 1 - (0.95)^10

Similar question to practice: a-string-of-10-light-bulbs-is-wired-in-such-a-way-that-if-131205.html
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: A string of 10 lightbulbs is wired in such a way that if any  [#permalink]

### Show Tags

19 Aug 2015, 22:54
1
crackgmat15 wrote:
VeritasPrepKarishma wrote:
tonytran14896 wrote:
A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period?
a. 0.05
b. (0.05)^10
c. 1 - (0.05)^10
d. (0.95)^10
e. 1 - (0.95)^10

Think about it: When will the string of lightbulbs not fail? Only when all lightbulbs stay alive simultaneously.

P (a lightbulb will stay alive) = 1 - 0.05 = 0.95

So probability that all lightbulbs stay live simultaneously $$= 0.95 * 0.95 * 0.95.....0.95 = (0.95)^{10}$$
(0.95s will be multiplied because it is an "and" situation. You need the first "and" the second "and" the third etc to stay alive)

asking this out of curiosity .what will be the question if the answer would be c .
my thinking is a bit weird please forgive me.

.05 is the probability of a light bulb failing.
(.05)^10 is the probability of EVERY light bulb failing.

1 - (.05)^10 is the probability that not every light bulb fails.

In a situation like this, you could use it:
A room has 10 light bulbs and a weaver needs to weave a cloth there this evening. He needs at least one light bulb working to weave. What is the probability that he will be able to weave?
_________________
Karishma
Veritas Prep GMAT Instructor

Non-Human User
Joined: 09 Sep 2013
Posts: 13412
Re: A string of 10 lightbulbs is wired in such a way that if any  [#permalink]

### Show Tags

29 Jan 2018, 08:09
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 lightbulbs is wired in such a way that if any   [#permalink] 29 Jan 2018, 08:09
Display posts from previous: Sort by