Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 563 reviewsTarget Test Prep

Probability Question

Expert replies
Post new topic Post Reply
Subscribe topic
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 23
Joined: Wed Sep 14, 2011 12:34 am
by seema19 » Mon Oct 03, 2011 10:57 pm
A box contains 12 bulbs, of which 4 are defective. 3 bulbs are selected at random and inserted into 3 sockets in a room. Find the probability that the room is lit.

a) 4/55
b) 1/55
c) 54/55
d) 1/4
e) 2/55

Answer: [spoiler]54/55[/spoiler]

This is how I solved it:
Out of the 12 bulbs, 4 are defective. Thus, the remaining 8 are good. Now, we have to choose 3 bulbs out of the 8 good bulbs so that the room is lit - 8C3/12C3 - But, this was wrong as I got the answer as 14/55. Can someone please let me know where I am going wrong.
Top
Join the discussion
Source: — Problem Solving |
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members
Thanked: 230 times

by shankar.ashwin » Mon Oct 03, 2011 11:04 pm
for the room to be lit, it is sufficient that atleast 1 bulb is lit (not necessary all 3 should work)

So find, 1 - P(all 3 are defective)

1 - 4C3/12C3 = 54/55
Top
Join the discussion
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members
Thanked: 114 times

by knight247 » Mon Oct 03, 2011 11:07 pm
The concept u need to understand is that for the room to be lit, having only one working bulb is also sufficient. Its not necessary that all three bulbs have to be working. Let W stand for working and D stand for defective. So we could have (DWW)3!/2!+(DDW)3!/2!+(WWW). What this translates into is, If three bulbs are picked up at random, what is the probability that atleast one works. Since the above calculation is a bit time consuming we can find the complementary i.e. the probability that no bulb works out of the three picked up.

# of possible outcomes=12C3=220
Number of ways to pick only 3 defective bulbs=4C3=4
Probability=4/220=1/55

Now, 1-1/55=54/55 Hence C
Top
Join the discussion