BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

probability that the plane will crash

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 117
Joined: Wed Dec 30, 2009 1:57 pmFollowed by: 1 member
Location: India
Thanked: 4 times
by abhi332 » Thu Feb 25, 2010 1:17 pm
A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines
are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one
will fail. There is a 75% probability that engine two will work. The third engine works only half the time. What is
the probability that the plane will crash in any given flight?
(A) 7/12
(B) 1/4
(C) 1/2
(D) 7/24
(E) 17/24
[spoiler]
OA:D[/spoiler]
What you think, you become.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members
Location: India
Thanked: 64 times
GMAT Score:760

by harsh.champ » Thu Feb 25, 2010 1:33 pm
abhi332 wrote:A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines
are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one
will fail. There is a 75% probability that engine two will work. The third engine works only half the time. What is
the probability that the plane will crash in any given flight?
(A) 7/12
(B) 1/4
(C) 1/2
(D) 7/24
(E) 17/24
[spoiler]
OA:D[/spoiler]
We have to consider 2 cases:-1)When 2 engines have failed
2)When all 3 engines have failed
Case 1:-Probability that the plane will crash = 1/3 x 1/4 x1/2 + 2/3 x 1/4 x 1/2 + 1/3 x 3/4 x 1/2 = 7/24

Hey abhi,
I wanted to ask why don't we consider the Case 2??
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 117
Joined: Wed Dec 30, 2009 1:57 pmFollowed by: 1 member
Location: India
Thanked: 4 times

by abhi332 » Thu Feb 25, 2010 1:41 pm
you don't have consider 2nd one because if 2 engine fails than plane will surely crash.

No need to consider when all engine fails.
What you think, you become.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 117
Joined: Wed Dec 30, 2009 1:57 pmFollowed by: 1 member
Location: India
Thanked: 4 times

by abhi332 » Thu Feb 25, 2010 1:45 pm
Hey Harsh, I am not sure..
What you think, you become.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 117
Joined: Wed Dec 30, 2009 1:57 pmFollowed by: 1 member
Location: India
Thanked: 4 times

by abhi332 » Thu Feb 25, 2010 1:49 pm
hey harsh,

Are you sure calculation is correct
Probability that the plane will crash = 1/3 x 1/4 x1/2 + 2/3 x 1/4 x 1/2 + 1/3 x 3/4 x 1/2
I am getting 0.25

but the ans is 0.29
What you think, you become.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members
Location: India
Thanked: 64 times
GMAT Score:760

by harsh.champ » Thu Feb 25, 2010 2:38 pm
abhi332 wrote:Hey Harsh, I am not sure..
I guess we need help from some expert over here.
Whats the source??
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members
Location: India
Thanked: 64 times
GMAT Score:760

by harsh.champ » Thu Feb 25, 2010 2:40 pm
abhi332 wrote:you don't have consider 2nd one because if 2 engine fails than plane will surely crash.

No need to consider when all engine fails.
But still,that would be a different case,
so why should we leave it??
Even if all 3 fails ,still the plane will crash.
According to me,the OA is wrong or the question framed very poorly...
Whatever be the case,I dont think such ambiguous questions can appear on test-day.
Wat-say??
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members
Location: India
Thanked: 64 times
GMAT Score:760

by harsh.champ » Thu Feb 25, 2010 2:43 pm
abhi332 wrote:hey harsh,

Are you sure calculation is correct
Probability that the plane will crash = 1/3 x 1/4 x1/2 + 2/3 x 1/4 x 1/2 + 1/3 x 3/4 x 1/2
I am getting 0.25

but the ans is 0.29
Dr. =24
Nr. = 1+2+3 =6 :!:

Hey,we have to consider the 3rd case over here.
Got it.
Chalo, atleast my concept was right,if not the calculation :mrgreen:
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 117
Joined: Wed Dec 30, 2009 1:57 pmFollowed by: 1 member
Location: India
Thanked: 4 times

by abhi332 » Thu Feb 25, 2010 2:45 pm
Following cases were considered while solving this question in the actual explanation

CASE ONE: Engine 1 fails, Engine 2 fails, Engine 3 works
CASE TWO: Engine 1 fails, Engine 2 works, Engine 3 fails
CASE THREE: Engine 1 works, Engine 2 fails, Engine 3 fails
CASE FOUR: Engine 1 fails, Engine 2 fails, Engine 3 fails
What you think, you become.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members
Location: India
Thanked: 64 times
GMAT Score:760

by harsh.champ » Thu Feb 25, 2010 2:47 pm
abhi332 wrote:Following cases were considered while solving this question in the actual explanation

CASE ONE: Engine 1 fails, Engine 2 fails, Engine 3 works
CASE TWO: Engine 1 fails, Engine 2 works, Engine 3 fails
CASE THREE: Engine 1 works, Engine 2 fails, Engine 3 fails
CASE FOUR: Engine 1 fails, Engine 2 fails, Engine 3 fails
Look at the 4th case.
It's the same as mine.
I guess we do have to take the 4th case over here.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 1302
Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members
Location: Toronto
Thanked: 539 times
GMAT Score:800

by Testluv » Thu Feb 25, 2010 7:11 pm
In these scenario or case probability questions, you want to think hard about the different ways the desirable event can occur.

What's the desirable event here?
...the plane crashing.

How can the plane crash?

If at least 2 engines fail...so if 2 or 3 engines fail.

How can 2 engines fail?

If the first and second fail OR if the first and third fail OR if the second and third fail.

That's three cases. And of course there's only one case for all 3 engines failling...that's a total of four cases.

The reason we have to consider this fourth case is that the three engines might fail simultaneously rather than sequentially...in other words, we can't just assume that the engines fail in sequence. If all three engines fail at the same time, then that is a distinct case from where only two of the engines are failing.
Kaplan Teacher in Toronto
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 117
Joined: Wed Dec 30, 2009 1:57 pmFollowed by: 1 member
Location: India
Thanked: 4 times

by abhi332 » Fri Feb 26, 2010 1:07 am
Thanks Testluv, I understood this now clearly :)
What you think, you become.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8137
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Mon Dec 18, 2017 9:01 am
abhi332 wrote:A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 75% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?
(A) 7/12
(B) 1/4
(C) 1/2
(D) 7/24
(E) 17/24
We are given that a plane will stay in the air as long as at least two of the three engines are working. So, to determine the probability that the plane will crash, we need to determine the probability that at least two of the three engines are not working.

The probability of engine one not working is 1/3, the probability of engine two is not working is 1/4, and the probability of engine 3 not working is 1/2.

Scenario 1:

1 does not work, 2 does not work, 3 works

1/3 x 1/4 x 1/2 = 1/24

Scenario 2:

1 does not work, 2 works, 3 does not work

1/3 x 3/4 x 1/2 = 3/24

Scenario 3:

1 works, 2 does not work, 3 does not work

2/3 x 1/4 x 1/2 = 2/24

Scenario 4:

1 does not work, 2 does not work, 3 does not work

1/3 x 1/4 x 1/2 = 1/24

Thus, the probability that the plane will crash is 1/24 + 3/24 + 2/24 + 1/24 = 7/24.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1