GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2019, 22:33

### 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

# A box contains three red marbles and 1 green marble. If the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 475
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
A box contains three red marbles and 1 green marble. If the  [#permalink]

### Show Tags

Updated on: 11 Oct 2013, 02:39
2
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:12) correct 24% (01:23) wrong based on 171 sessions

### HideShow timer Statistics

A box contains three red marbles and 1 green marble. If the marbles are removed from the box one at a time, in random order, what is the probability that all three red marbles are removed before the green marble?

(A) $$\frac{1}{64}$$

(B) $$\frac{1}{24}$$

(C) $$\frac{1}{12}$$

(D) $$\frac{1}{4}$$

(E) $$\frac{1}{2}$$

Originally posted by avohden on 10 Oct 2013, 14:49.
Last edited by Bunuel on 11 Oct 2013, 02:39, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Joined: 11 Jan 2012
Posts: 8
Location: India
Concentration: Operations, Finance
GMAT Date: 08-31-2012
GPA: 3.7
Re: A box contains three red marbles and 1 green marble.  [#permalink]

### Show Tags

10 Oct 2013, 21:20
1
It is 3/4*2/3*1/2 = 1/4
Senior Manager
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 475
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Re: A box contains three red marbles and 1 green marble.  [#permalink]

### Show Tags

22 Oct 2013, 08:43
1
2
Official Explanation -

Answer D
There are 3 red marbles and 4 marbles total, so the probability of drawing a red marble on the first draw is 3/4 . On the second draw there are 2 red marbles and three marbles total so the probability of drawing a red marble is 2/3. On the third draw, there is only one red marble and one green marble, so the probability of drawing the red marble is 1/2. The probability of all three events happening is the product of the probabilities,$$\frac{3}{4}* \frac{2}{3} *\frac{1}{2}or \frac{1}{4}$$.

Hope it helps.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: A box contains three red marbles and 1 green marble. If the  [#permalink]

### Show Tags

31 Aug 2018, 06:57
avohden wrote:
A box contains three red marbles and 1 green marble. If the marbles are removed from the box one at a time, in random order, what is the probability that all three red marbles are removed before the green marble?

(A) $$\frac{1}{64}$$

(B) $$\frac{1}{24}$$

(C) $$\frac{1}{12}$$

(D) $$\frac{1}{4}$$

(E) $$\frac{1}{2}$$

GMATH´s method suggests avoiding the "partial probabilities sequences" (correctly used in the previous posts) because:

1. The justification for its validity is out-of-GMAT´s scope (conditional probabilities, NOT independency).
2. There are some problems in which students usually fall into "traps".

All that mentioned, let´s see how we would deal with this problem!

$$3\,{\text{red}}\,\,,\,\,1\,\,{\text{green}}$$

$$? = P\left( {{\text{green}}\,\,{\text{last,}}\,\,{\text{in}}\,\,{\text{4}}\,\,{\text{sequential}}\,\,{\text{extractions}}} \right)$$

$${\text{total}} = 4!\,\,\,\,\left( {{\text{equiprobables}}} \right)$$

$${\text{favorable}}\,\,{\text{ = }}\,\,{\text{3!}}\,\,\,\,\,\,\left( {{P_3}\,\,{\text{in}}\,\,{\text{first}}\,\,{\text{3}}\,\,{\text{red}}\,\,{\text{extractions}}} \right)$$

$$? = \frac{{3!}}{{4!}} = \frac{1}{4}$$

The above follows the notations and rationale taught in the GMATH method.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: A box contains three red marbles and 1 green marble. If the   [#permalink] 31 Aug 2018, 06:57
Display posts from previous: Sort by

# A box contains three red marbles and 1 green marble. If the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne