Last visit was: 19 Nov 2025, 05:27 It is currently 19 Nov 2025, 05:27
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2 
655-705 Level|   Probability|      
User avatar
Temurkhon
User avatar
Joined: 23 Jan 2013
Last visit: 06 Apr 2019
Posts: 412
Own Kudos:
314
Given Kudos: 43
Schools: Cambridge'16
Schools: Cambridge'16
Posts: 412
Kudos: 314
A bag contains 3 white balls, 3 black balls & 2 red balls 02 Aug 2015, 05:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
First option (first two balls are not red and the last is red): 6/8*5/7*2/6=5/28

Second option (first or second ball is red and the last is red): (6/8*2/7*1/6)*2=2/28

So, 5/28+2/28=7/28=1/4

A
avatar
oanhnguyen1116
avatar
Joined: 07 Jan 2016
Last visit: 19 Jun 2016
Posts: 14
Own Kudos:
45
Given Kudos: 29
Schools: AGSM '18
Schools: AGSM '18
Posts: 14
Kudos: 45
A bag contains 3 white balls, 3 black balls & 2 red balls 13 Mar 2016, 07:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Could you tell me more about your way to give that formula? Thank you.

zisis
Bunuel
krishan
A bag contains 3 white balls, 3 black balls & 2 red balls. One by one three balls are drawn out without replacement. What is the probability that the third ball is red?

A. 0.25
B. 0.15
C. 0.35
D. 0.45
E. 0.40

Thanks

The initial probability of drawing red ball is 2/8. Without knowing the other results, the probability of drawing red ball will not change for ANY successive drawing: second, third, fourth...

Similar problems:
ps-probability-gmat-made-me-lose-my-marbles-36830.html?hilit=initial%20draw
probability-of-picking-last-97015.html?hilit=initial%20probability
probability-question-please-solve-90272.html?hilit=initial%20probability#p686028

Hope it's clear.

!!!!!
went the long way - still under 2min

RedOtherRed +OtherRR+OOR

\(\frac{1}{28}+\frac{1}{28}+\frac{5}{28}=\frac{7}{28}=\frac{1}{4}\)
Show more
avatar
SagarV
avatar
Joined: 11 Jan 2021
Last visit: 04 Jun 2021
Posts: 4
Given Kudos: 20
Posts: 4
Kudos: 0
A bag contains 3 white balls, 3 black balls & 2 red balls 26 Feb 2021, 10:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello, please help me too:

As per my logic: P (last ball is Red) = 1 - P(First 2 balls are red)

= 1 - ( (2 / 8) * (1/7) )
= 1 - (1/28)
= 27 / 28
= 0.96

Where am I wrong ?
Thanks :)
User avatar
Regor60
User avatar
Joined: 21 Nov 2021
Last visit: 17 Nov 2025
Posts: 528
Own Kudos:
383
Given Kudos: 459
Posts: 528
Kudos: 383
A bag contains 3 white balls, 3 black balls & 2 red balls 26 Apr 2022, 08:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How many ways to arrange the 8 balls ?

8!/3!3!2! = 540 > Permutation eliminating duplicate colors

How many ways to arrange the balls where a red is in the third position ?

Arrange remaining 7 balls

7!/3!3! = 140

Probability 140/560 = 1/4

Posted from my mobile device
User avatar
tusharsajeev08
User avatar
Joined: 29 Aug 2024
Last visit: 09 Jan 2025
Posts: 4
Own Kudos:
1
Given Kudos: 378
Posts: 4
Kudos: 1
A bag contains 3 white balls, 3 black balls & 2 red balls 08 Oct 2024, 10:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
  1. All the balls except one red ball: 7/8
  2. Since 1 ball is selected we are left with: 6/7
  3. Last is to select 1 Red ball amongst 2 Red balls (since we don't know which was selected in "7/8") : 2/6

7/8*6/7*2/6 =1/4

ans: 25%
User avatar
MBhavya
User avatar
Joined: 28 May 2023
Last visit: 19 Nov 2025
Posts: 17
Own Kudos:
8
Given Kudos: 171
Location: India
Schools: IESE '27 (D) Bocconi (D)
GMAT Focus 1: 595 Q82 V81 DI76
GPA: 8.32
WE:Business Development (Non-Profit)
Schools: IESE '27 (D) Bocconi (D)
GMAT Focus 1: 595 Q82 V81 DI76
Posts: 17
Kudos: 8
A bag contains 3 white balls, 3 black balls & 2 red balls 12 Oct 2024, 22:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This is how I solved it. There could be 3 type of cases of getting red in 3rd pick when picking 3 balls without replacement.

Case 1:
Not Red _ Not Red _ Red
6/8 * 5/7 * 2/6 = 5/28

Case 2:
Red _ Not Red _ Red
2/8 * 6/7 * 1/6 = 1/28

Case 3
Not Red _ Red _ Red
6/8 * 2/7 * 1/6 = 1/28

Adding Case 1,2,3
5/28 + 1/28 + 1/28 = 7/28 = 1/4 or 0.25

Thus, answer is option A (0.25).
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,584
Own Kudos:
1,079
Posts: 38,584
Kudos: 1,079
A bag contains 3 white balls, 3 black balls & 2 red balls 17 Oct 2025, 09:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
   1   2 
Moderators:
Bunuel
Math Expert
105385 posts
Krunaal
Tuck School Moderator
805 posts