Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
27 Apr 2017, 22:48
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
31% (02:51) correct
69%
(02:16)
wrong
based on 439
sessions
History
Date
Time
Result
Not Attempted Yet
A bag contains 10 bulbs and 5 torches, out of which 3 bulbs and 2 torches are defective. If a person takes out two items from the bag at random, what is the probability that both are bulbs or both are in working condition?
A. 8/35
B. 3/7
C. 23/35
D. 6/7
E. None of these
A. 8/35
B. 3/7
C. 23/35
D. 6/7
E. None of these
Thanks,
Saquib
Quant Expert
e-GMAT
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
Saquib
Quant Expert
e-GMAT
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
13 Jul 2017, 19:31
Kudos
Bookmarks
This is how I process this problem:
We have:
----------Working------Defective-----Total
Bulb--------7---------------3-----------10
Torch-------3---------------2------------5
Total-------10--------------5-----------15
As you can see, there is an overlap between bulbs and working, which should be excluded.
Thus, P = P (both are bulbs) + P (both working) - P (both bulbs AND working).
1. P (both are bulbs):
10/15*9/14=3/7
2. P (both working):
10/15*9/14=3/7
3. P (both bulbs AND working):
7/15*6/14=1/5
P = 3/7+3/7-1/5=23/35
It is similar to what has been presented by others, however, I just thought setting up a table makes is easier to analyze this problem.
We have:
----------Working------Defective-----Total
Bulb--------7---------------3-----------10
Torch-------3---------------2------------5
Total-------10--------------5-----------15
As you can see, there is an overlap between bulbs and working, which should be excluded.
Thus, P = P (both are bulbs) + P (both working) - P (both bulbs AND working).
1. P (both are bulbs):
10/15*9/14=3/7
2. P (both working):
10/15*9/14=3/7
3. P (both bulbs AND working):
7/15*6/14=1/5
P = 3/7+3/7-1/5=23/35
It is similar to what has been presented by others, however, I just thought setting up a table makes is easier to analyze this problem.
01 May 2017, 05:24
Kudos
Bookmarks
I am quite happy with the discussion so far for this question. While posting this question, I was expecting a few of you might fall into the trap and make mistake in either –
Let me explain the way I solve this question –
Thanks,
Saquib
Quant Expert
e-GMAT
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
- 1. Considering Permutation instead of just Combination
2. Making a mistake while choosing the two items – a few of you might not consider all the working condition cases or miss out on subtracting a few additional cases.
Let me explain the way I solve this question –
- • We need to choose 2 items from 15 items, that can be done in \(^{15}C_2\) ways \(= 15*\frac{14}{2} = 15*7= 105\) ways.
• We need to find the probability that
- o Either both are bulbs –(Case 1)
- That can be chosen in \(^{10}C_2\) ways \(= 10*\frac{9}{2} = 45\) ways
Now please understand that in these 45 ways, we have considered all type of cases – both the bulbs working OR 1 bulb working and 1 being defective OR both are defective since in this case, we were choosing the bulbs without any restrictions.
So again just for everyone’s clarity
45 ways consists of – [both bulbs working OR 1 working 1defective OR both defective]
o Now that we have considered the cases of both are bulbs, lets us focus on both items are in the working condition.(Case 2)
- Now there are total (10-3) =7 bulbs and (5-2) = 3 torches which are working
That means total (7+3) = 10 items are working.
We need to choose 2 of them, we can do that in \(^{10}C_2\) ways \(= 45\) ways.
o Now focus on the bold part in Case 1, we are choosing both working bulbs in case 1 also and case 2 also, we are double counting it, so we need to subtract it once
Out of 7 bulbs, we can choose 2 working bulbs in \(^7C_2\)ways = 21 ways.
• Therefore, now we can say, the total ways of choosing either both bulbs or both in working condition are = 45 + 45 – 21 = 69 ways.
• Hence the probability \(= \frac{69}{105} = \frac{23}{35}\)
Thanks,
Saquib
Quant Expert
e-GMAT
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
