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

Redeem

Probability of Pulling out a blue marble exactly 3 times

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Thu Nov 28, 2013 10:57 am

Probability of Pulling out a blue marble exactly 3 times

by Mustcrackgmat » Sun Dec 22, 2013 8:55 am
A jar contains marbles of several different colors. Some marbles are to be taken from the jar one at a time, examined and the put back in the jar. What is the probability that exactly three of next five marbles taken from the jar will be blue?

(1) The probability that all of the next five marbles taken from the jar are blue is 243/3125.

(2) The probability that none of the next five marbles taken from the jar are blue is 32/3125.

Statement 2 gives me the prob of one single marble NOT being blue. How can statement 2 help me calculating the prob of marble BEING blue? There are seven colors, so am not sure if I can apply 1-2/5 logic here.
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Dec 22, 2013 9:23 am
Mustcrackgmat wrote:A jar contains marbles of several different colors. Some marbles are to be taken from the jar one at a time, examined and the put back in the jar. What is the probability that exactly three of next five marbles taken from the jar will be blue?

(1) The probability that all of the next five marbles taken from the jar are blue is 243/3125.

(2) The probability that none of the next five marbles taken from the jar are blue is 32/3125.

Statement 2 gives me the prob of one single marble NOT being blue. How can statement 2 help me calculating the prob of marble BEING blue? There are seven colors, so am not sure if I can apply 1-2/5 logic here.
P(blue) + P(not blue) = 1.
Let P(blue) = x/y and P(not blue) = a/b.
Thus:
x/y + a/b = 1.

Statement 1: The probability that all of the next five marbles taken from the jar are blue is 243/3125.
Since P(blue) = x/y, we get:
(x/y) * (x/y) * (x/y) * (x/y) * (x/y) = 243/3125
(x/y)� = 243/3125
x/y = 3/5.
Since we know that P(blue) = x/y = 3/5, we can determine the probability that exactly three of the next five marbles taken from the jar will be blue.
SUFFICIENT.

Statement 2: The probability that none of the next five marbles taken from the jar are blue is 32/3125.
Since P(not blue) = a/b, we get:
(a/b) * (a/b) * (a/b) * (a/b) * (a/b) = 32/3125
(a/b)� = 32/3125
a/b = 2/5.
Since x/y + a/b = 1, we get:
x/y = 1 - a/b = 1 - 2/5 = 3/5.
Since we know that P(blue) = x/y = 3/5, we can determine the probability that exactly three of the next five marbles taken from the jar will be blue.
SUFFICIENT.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Senior | Next Rank: 100 Posts
Posts: 61
Joined: Sat Aug 17, 2013 8:53 am
Thanked: 10 times

by dominhtri1995 » Sun Dec 22, 2013 10:06 am
Hi GuruNY

I have a question. How can you know that the probability will not change after a marble is taken out ?


Regard,
Top
Master | Next Rank: 500 Posts
Posts: 381
Joined: Wed May 19, 2010 10:15 pm
Thanked: 41 times
Followed by:2 members

by AbhiJ » Sun Dec 22, 2013 10:43 am
because you are replacing marbles.
Top
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Thu Nov 28, 2013 10:57 am

by Mustcrackgmat » Mon Dec 23, 2013 8:18 am
Hi GuruNY

With the help of statement 2, I can find the prob of pulling put at least one blue marble. How does this help me find the prob of pulling out exactly 3? I can pull out at least 3 marbles or maybe more? I am not clear on this?
Top
Post new topic Post Reply
• Page 1 of 1