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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
05 Oct 2012, 09:26

Expert's post

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

66% (04:45) correct
34% (03:50) wrong based on 59 sessions

Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions:

1) C1, if the paint contains 2 jars of brown paint and no blue paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of blue paint 4) J2, if the paint contains exactly 1 jar of blue paint

What is the probability that the new colour will be a shade of J (J1 or J2)?

(A) 75/84 (B) 10/21 (C) 17/42 (D) 11/21 (E) 37/42

For me is a good question, maybe time consuming because when you understand what is asked, the question must be set-up carefully.

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
05 Oct 2012, 12:21

[/spoiler]

carcass wrote:

Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no blue paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of blue paint 4) J2, if the paint contains exactly 1 jar of blue paint What is the probability that the new colour will be a shade of J (J1 or J2)? (A) 75/84 (B) 10/21 (C) 17/42 (D) 11/21 (E) 37/42

For me is a good question, maybe time consuming because when you understand what is asked, the question must be set-up carefully.

Let me know

Probability of J=Probability of J1 + J2

Probability of J1=((4c2*5c1) + (4c3))/(9c4)----------------atleast 2 so it can be 2 blue or 3 blue solving we get. =(17/42)

Probability of J2=(4c1*5c2)/(9c4) solving we get =(20/42) Probability of j=(17/42) + (20/42) =37/42

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
05 Oct 2012, 14:36

6

This post received KUDOS

carcass wrote:

Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no blue paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of blue paint 4) J2, if the paint contains exactly 1 jar of blue paint What is the probability that the new colour will be a shade of J (J1 or J2)? (A) 75/84 (B) 10/21 (C) 17/42 (D) 11/21 (E) 37/42

For me is a good question, maybe time consuming because when you understand what is asked, the question must be set-up carefully.

Let me know

If the new color doesn't contain Blue paint, then it isn't of type J. So, it is much easier to calculate the complementary probability. P(no Blue paint chosen) = (5/9)*(4/8)*(3/7) = 5/42. Therefore, the required probability is 1 - 5/42 = 37/42.

Answer E. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: Charlie, a painter, has 9 jars of paint…700 Level PS [#permalink]
12 Apr 2013, 20:12

Solution 1: Number of ways of making J1 = number of ways of choosing the paints such that there are two blue paints + number of ways of choosing the paints such that there are three blue paints = 4C2 x 5C1 + 4C3 = 34

Number of ways of making J2 = number of ways of choosing the paints such that there is one jar of blue and two jars of any other color = 4C1 x 5C2 = 40

Number of ways of combining three paints to make a color = 9C3 = 84

Number of ways (new color will be a shade of J1 or J2) = n(J1) + n(J2) - n(J1 n J2) = n(J1) + n(J2) as n(J1 n J2) = 0 [either there will be exactly one color of blue or two or more]

Therefore probability (new color will be a shade of J1 or J2) = (40+34)/84 = 74/84 = 37/42 Option E

Solution 2: Looking at the classifications, we realize straight away that J1 or J2 = number of ways of selecting the paints such that there is at least one blue paint included Therefore probability = 1 - prob. (no blue paint is included) = 1 - (5C3/9C3) = 1 - 10/84 = 74/84 = 37/42 Option E _________________

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
13 Apr 2013, 12:42

Think about it like this: the question is asking for the probability that we have three jars of paint, none of which are blue.

Thus, it is basically an "at least" question, which invariably implies 1 (full probability) - (probability of the inverse occurrence).

That is, if you want the probability that a coin flipped three times will land on Heads at least once, calculate the probability of landing ONLY ON TAILS (=1/8) and subtract it to find the "at least once" situation.

1 - 1/8 = 7/8 chance that it will land on Heads at least once.

So it is simplest to think about it as asking "what is the probability that the mix will have at least one jar of blue paint in it?"

The probability of having no jars of blue paint is (-B)(-B)(-B) = (5/9)(4/8)(3/7), which reduces to 5/42.

That is, 1 - no blue = 1 - (-B)(-B)(-B) = 1 - 5/42 = 37/42. The answer is E. _________________

Looking to Maximize your GMAT Score in a Minimum of Time? PM ME!

I am Rowan Hand, a London GMAT Tutor, Consultant, and Coach. Based in the UK--available anywhere!

Re: Charlie, a painter, has 9 jars of paint: 4 are blue, 2 are y [#permalink]
16 Jul 2014, 13:29

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. _________________

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

In out-of-the-way places of the heart, Where your thoughts never think to wander, This beginning has been quietly forming, Waiting until you were ready to emerge. For a long...