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

 It is currently 20 Jun 2018, 23:07

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

There are 5 different coloured balls in a bag. A ball is chosen and re

Author Message
TAGS:

Hide Tags

Intern
Joined: 13 Nov 2010
Posts: 2
There are 5 different coloured balls in a bag. A ball is chosen and re [#permalink]

Show Tags

13 Nov 2010, 10:04
1
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (00:13) wrong based on 4 sessions

HideShow timer Statistics

There are 5 different coloured balls in a bag. A ball is chosen and replaced 4 times. What is the probability that:

all the balls chosen are different colours?
2 of the balls are the same colour?
3 of the balls are the same colour?
all the balls are the same colour?

Working out the all same and all different is not too hard but is there a quick way to do the other parts without drawing the 625 branch tree diagram?
Manager
Joined: 16 Oct 2010
Posts: 83
Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 700 Q49 V35
WE: Information Technology (Investment Banking)
Re: There are 5 different coloured balls in a bag. A ball is chosen and re [#permalink]

Show Tags

14 Nov 2010, 00:12
greed1 wrote:
Hi I was wondering if anyone knows how to work this question out:

There are 5 different coloured balls in a bag. A ball is chosen and replaced 4 times. What is the probability that:

all the balls chosen are different colours?
2 of the balls are the same colour?
3 of the balls are the same colour?
all the balls are the same colour?

Working out the all same and all different is not too hard but is there a quick way to do the other parts without drawing the 625 branch tree diagram?

I would like to give it a try.
1) All of the balls cosen are of different color
P = 5/5 * 4/5 * 3/5 * 2 /5 = 24/125

2) p = 5/5 * 1/5 * 4/5 * 3/5 * 4C2 = 72/125

3) p = 5/5 * 1/5 * 1/5 * 4/5 * 4C3 = 16/125

4) p = 5/5 * 1/5 * 1/5 * 1/5 = 1/125
Intern
Joined: 13 Nov 2010
Posts: 2
Re: There are 5 different coloured balls in a bag. A ball is chosen and re [#permalink]

Show Tags

14 Nov 2010, 02:28
1
syog wrote:
greed1 wrote:
Hi I was wondering if anyone knows how to work this question out:

There are 5 different coloured balls in a bag. A ball is chosen and replaced 4 times. What is the probability that:

all the balls chosen are different colours?
2 of the balls are the same colour?
3 of the balls are the same colour?
all the balls are the same colour?

Working out the all same and all different is not too hard but is there a quick way to do the other parts without drawing the 625 branch tree diagram?

I would like to give it a try.
1) All of the balls cosen are of different color
P = 5/5 * 4/5 * 3/5 * 2 /5 = 24/125

2) p = 5/5 * 1/5 * 4/5 * 3/5 * 4C2 = 72/125

3) p = 5/5 * 1/5 * 1/5 * 4/5 * 4C3 = 16/125

4) p = 5/5 * 1/5 * 1/5 * 1/5 = 1/125

The right method. Your answers add up to 113/125, so what would account for the remaining 12/125?
Retired Moderator
Joined: 02 Sep 2010
Posts: 775
Location: London
Re: There are 5 different coloured balls in a bag. A ball is chosen and re [#permalink]

Show Tags

14 Nov 2010, 03:15
1
greed1 wrote:
Hi I was wondering if anyone knows how to work this question out:

There are 5 different coloured balls in a bag. A ball is chosen and replaced 4 times. What is the probability that:

all the balls chosen are different colours?
2 of the balls are the same colour?
3 of the balls are the same colour?
all the balls are the same colour?

Working out the all same and all different is not too hard but is there a quick way to do the other parts without drawing the 625 branch tree diagram?

1) All balls of different colors --> (5/5) * (4/5) * (3/5) * (2/5) = (24/125)

2) 2 balls of the same color --> ((pick the color to be repeated twice) * (pick the other 2 color) * (number of permutations))/(Total permutations) = (5 * C(4,2) * (4!/2!))/(5^4) = (72/125)

3) 3 balls of the same color --> ((pick the common color) * (pick the other color) * (number of permutations))/(total permutations) = (5 * C(4,1) * (4!/3!))/5^4 = (16/125)

4) All same color --> Only 1 such combination possible for each color, there are 5 colors, so total probability = 5/5^4 = (1/125)

5) Two balls of one color and two of another color --> ((choose 2 colors) * (permute))/(total permutations) = C(5,2) * (4!/2!2!) / 5^4 = (12/125)

Total probability for all cases = 1
_________________
Manager
Joined: 16 Oct 2010
Posts: 83
Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 700 Q49 V35
WE: Information Technology (Investment Banking)
Re: There are 5 different coloured balls in a bag. A ball is chosen and re [#permalink]

Show Tags

14 Nov 2010, 03:28
1
greed1 wrote:
syog wrote:
greed1 wrote:
Hi I was wondering if anyone knows how to work this question out:

There are 5 different coloured balls in a bag. A ball is chosen and replaced 4 times. What is the probability that:

all the balls chosen are different colours?
2 of the balls are the same colour?
3 of the balls are the same colour?
all the balls are the same colour?

Working out the all same and all different is not too hard but is there a quick way to do the other parts without drawing the 625 branch tree diagram?

I would like to give it a try.
1) All of the balls cosen are of different color
P = 5/5 * 4/5 * 3/5 * 2 /5 = 24/125

2) p = 5/5 * 1/5 * 4/5 * 3/5 * 4C2 = 72/125

3) p = 5/5 * 1/5 * 1/5 * 4/5 * 4C3 = 16/125

4) p = 5/5 * 1/5 * 1/5 * 1/5 = 1/125

The right method. Your answers add up to 113/125, so what would account for the remaining 12/125?

as suggested above, the remaining 12/125 is the probability of getting 2 balls of one colour and another 2 balls of another one colur.

p = 5/5 * 1/5 * 4/5 * 1/5 * 4C2/2 = 12/125

When we say probability of getting 2 balls of one colour, it inherently means that remaining balls are of different colours.
Non-Human User
Joined: 09 Sep 2013
Posts: 7011
Re: There are 5 different coloured balls in a bag. A ball is chosen and re [#permalink]

Show Tags

01 Oct 2017, 06:09
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.
_________________
Re: There are 5 different coloured balls in a bag. A ball is chosen and re   [#permalink] 01 Oct 2017, 06:09
Display posts from previous: Sort by