GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 25Crafting an Impactful Resume: Balancing Detail with Brevity
10:00 AM EDT
-10:30 AM EDT
Showcase your achievements through impactful storytelling! Get ready for an LIVE session on April 25, Learn how to craft compelling narratives on your resume that resonate with admission committees.
Apr 26Get a Top GRE Score with Target Test Prep
12:00 PM EDT
-01:00 PM EDT
The Target Test Prep course represents a quantum leap forward in GRE preparation, a radical reinterpretation of the way that students should study. In fact, more and more Target Test Prep students are scoring 329 and above on the GRE.
A string of 10 lightbulbs is wired in such a way that if any
[#permalink]
07 Sep 2020, 04:45
07 Sep 2020, 04:45
Expert Reply
9
Bookmarks
00:00
Question Stats:
49% (01:05) correct
50% (01:02) wrong based on 175 sessions
Hide Show timer Statistics
A string of 10 lightbulbs is wired in such a way that if any individual lightbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during time period T is 0.06, what is the probability that the string of lightbulbs will fail during time period T ?
A. \(0.06\)
B. \((0.06)^{10}\)
C. \(1 - (0.06)^{10}\)
D. \((0.94)^{10}\)
E. \(1 - (0.94)^{10}\)
A. \(0.06\)
B. \((0.06)^{10}\)
C. \(1 - (0.06)^{10}\)
D. \((0.94)^{10}\)
E. \(1 - (0.94)^{10}\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A string of 10 lightbulbs is wired in such a way that if any
[#permalink]
07 Sep 2020, 06:00
07 Sep 2020, 06:00
6
1
Bookmarks
Carcass wrote:
A string of 10 lightbulbs is wired in such a way that if any individual lightbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during time period T is 0.06, what is the probability that the string of lightbulbs will fail during time period T ?
A. \(0.06\)
B. \((0.06)^{10}\)
C. \(1 - (0.06)^{10}\)
D. \((0.94)^{10}\)
E. \(1 - (0.94)^{10}\)
A. \(0.06\)
B. \((0.06)^{10}\)
C. \(1 - (0.06)^{10}\)
D. \((0.94)^{10}\)
E. \(1 - (0.94)^{10}\)
Aside: If P(bulb fails) = 0.06, then P(bulb doesn't fail) = 0.94
Okay, the entire string of lightbulbs will fail if 1 or more lightbulbs fail.
So, we want P(at least 1 lightbulb fails)
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
P(at least 1 lightbulb fails) = 1 - P(zero lightbulbs fail)
P(zero lightbulbs fail)
P(zero lightbulbs fail) = P(1st bulb doesn't fail AND 2nd bulb doesn't fail AND 3rd bulb doesn't fail AND . . . AND 9th bulb doesn't fail AND 10th bulb doesn't fail)
= P(1st bulb doesn't fail) x P(2nd bulb doesn't fail) x P(3rd bulb doesn't fail) x . . . x P(9th bulb doesn't fail) x P(10th bulb doesn't fail)
= (0.94) x (0.94) x (0.94) x . . . x(0.94) x (0.94)
= (0.96)^10
So, P(at least 1 lightbulb fails) = 1 - P(zero lightbulbs fail)
= 1 - (0.94)^10
Answer: E
Cheers,
Brent
General Discussion
Re: A string of 10 lightbulbs is wired in such a way that if any
[#permalink]
07 Sep 2020, 04:46
07 Sep 2020, 04:46
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
