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

 It is currently 18 Oct 2019, 19:37 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre

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

Hide Tags

Manager  Joined: 18 Feb 2015
Posts: 82
A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre  [#permalink]

Show Tags

4 00:00

Difficulty:   55% (hard)

Question Stats: 62% (01:51) correct 38% (01:56) wrong based on 167 sessions

HideShow timer Statistics

A bag contains 3 blue disks, 3 green disks and 4 orange disks. If three disks are selected random from the bag, what is the probability that 1 of the disks will be green and the other 2 of the disks will be orange?

A) 1/30
B) 1/20
C) 3/40
D) 1/10
E) 3/20

My solution:

Total disks: 10
The prob. of selecting a green=3/10
Once a green disk is selected, we are left with 9 total disks
Then the probability of selecting an orange disk = 4/9
Once one orange is selected, we are left with 8 total disks
Then the probability of selecting the second orange disk = 3/8

Total Probability = 3/10 * 4/9 * 3/8 ==> 1/20

However thats not the correct answer. What am I missing?

Thanks
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre  [#permalink]

Show Tags

2
2
HarveyKlaus wrote:
A bag contains 3 blue disks, 3 green disks and 4 orange disks. If three disks are selected random from the bag, what is the probability that 1 of the disks will be green and the other 2 of the disks will be orange?

A) 1/30
B) 1/20
C) 3/40
D) 1/10
E) 3/20

My solution:

Total disks: 10
The prob. of selecting a green=3/10
Once a green disk is selected, we are left with 9 total disks
Then the probability of selecting an orange disk = 4/9
Once one orange is selected, we are left with 8 total disks
Then the probability of selecting the second orange disk = 3/8

Total Probability = 3/10 * 4/9 * 3/8 ==> 1/20

However thats not the correct answer. What am I missing?

Thanks

Dear HarveyKlaus,
I'm happy to respond. One very tricky thing about probability is that, when a question asked about the probability of a certain result, we have to be careful not to assume that there is only one way to get that result. For example, you approach explicitly assumes that the green disk was selected first. What if it wasn't? You calculated the probability of getting to that result by a specific route, but this excludes other ways to get to that same result.

One way to approach this would be a kind of tree approach--ultimately, the choices, in order, could be GOO or OGO or OOG, and all three of those would have to be calculated and added.

P(GOO) = 1/20 (what you calculated)
P(OGO) = (4/10)*(3/9)*(3/8) = 1/20
P(OOG) = (4/10)*(3/9)*(3/8) = 1/20
P(total) = 3/20

Another approach would be to apply counting techniques. See:
GMAT Probability and Counting Techniques
Think of it this way. Suppose the discs are give letters, A - J. Discs A, B, & C are green. Discs D-G are orange, and rest are blue.
Question #1: how many different sets of three altogether could we pick? 10C3 = $$\frac{10!}{(7!)(3!)}$$ = $$\frac{10*9*8}{3*2*1}$$ = 10*3*4 = 120. That's the denominator.

Question #2: how many different sets of three involve just one green and two oranges? Three ways to choose the single green member, and 4C2 = 6 ways to choose the two orange members. By the Fundamental Counting Principle, number of ways = 3*6 = 18. That's the numerator.

Probability = 18/120 = 3/20

Here are a couple more blogs you may find helpful:
GMAT Data Sufficiency Practice Questions on Probability
GMAT Advanced Probability Problems

Does this make sense?
Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager  Joined: 18 Feb 2015
Posts: 82
Re: A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre  [#permalink]

Show Tags

Thank you Mike! Thats very helpful!

Best,
Harvey

mikemcgarry wrote:
HarveyKlaus wrote:
A bag contains 3 blue disks, 3 green disks and 4 orange disks. If three disks are selected random from the bag, what is the probability that 1 of the disks will be green and the other 2 of the disks will be orange?

A) 1/30
B) 1/20
C) 3/40
D) 1/10
E) 3/20

My solution:

Total disks: 10
The prob. of selecting a green=3/10
Once a green disk is selected, we are left with 9 total disks
Then the probability of selecting an orange disk = 4/9
Once one orange is selected, we are left with 8 total disks
Then the probability of selecting the second orange disk = 3/8

Total Probability = 3/10 * 4/9 * 3/8 ==> 1/20

However thats not the correct answer. What am I missing?

Thanks

Dear HarveyKlaus,
I'm happy to respond. One very tricky thing about probability is that, when a question asked about the probability of a certain result, we have to be careful not to assume that there is only one way to get that result. For example, you approach explicitly assumes that the green disk was selected first. What if it wasn't? You calculated the probability of getting to that result by a specific route, but this excludes other ways to get to that same result.

One way to approach this would be a kind of tree approach--ultimately, the choices, in order, could be GOO or OGO or OOG, and all three of those would have to be calculated and added.

P(GOO) = 1/20 (what you calculated)
P(OGO) = (4/10)*(3/9)*(3/8) = 1/20
P(OOG) = (4/10)*(3/9)*(3/8) = 1/20
P(total) = 3/20

Another approach would be to apply counting techniques. See:
GMAT Probability and Counting Techniques
Think of it this way. Suppose the discs are give letters, A - J. Discs A, B, & C are green. Discs D-G are orange, and rest are blue.
Question #1: how many different sets of three altogether could we pick? 10C3 = $$\frac{10!}{(7!)(3!)}$$ = $$\frac{10*9*8}{3*2*1}$$ = 10*3*4 = 120. That's the denominator.

Question #2: how many different sets of three involve just one green and two oranges? Three ways to choose the single green member, and 4C2 = 6 ways to choose the two orange members. By the Fundamental Counting Principle, number of ways = 3*6 = 18. That's the numerator.

Probability = 18/120 = 3/20

Here are a couple more blogs you may find helpful:
GMAT Data Sufficiency Practice Questions on Probability
GMAT Advanced Probability Problems

Does this make sense?
Mike Current Student B
Joined: 26 Jan 2016
Posts: 98
Location: United States
GPA: 3.37
Re: A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre  [#permalink]

Show Tags

Probability of Picking 1 green (3/10)*probability of orange (4/9)*probability of another orange (3/8)=1/20. There are three ways this can happen goo
ogo
oog
1/20*3=3/20
Senior Manager  G
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 277
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22 GPA: 3.7
WE: Information Technology (Consulting)
Re: A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre  [#permalink]

Show Tags

1
Probability of complex events = Individual Events * their arrangements.

In this case - it is equal to --
Probability of 1 green - 3/10
Probability of 1 orange - 4/9 (Since 1 green has already selected.)
Probability of 2nd orange - 3/8

Their arrangements = 3!/2!*1! = 3

Probability = 3/10*4/9*3/8*3 = 3/20
Intern  Joined: 18 Dec 2016
Posts: 18
Location: United Kingdom
GMAT 1: 690 Q47 V38 GPA: 4
WE: Investment Banking (Investment Banking)
Re: A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre  [#permalink]

Show Tags

Could you explain the part with " Their arrangements = 3!/2!*1! = 3 " ?

Thx
Senior Manager  G
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 277
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22 GPA: 3.7
WE: Information Technology (Consulting)
Re: A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre  [#permalink]

Show Tags

GMATforSeaCliff wrote:
Could you explain the part with " Their arrangements = 3!/2!*1! = 3 " ?

Thx

Sure. I meant the arrangements of the selected events i.e how many ways these events can arrange themselves. Total we have 3 events so the arrangement is 3! and out of them 2 are same i.e. selecting orange disk hence 3!/2!

Hope its clear.
Intern  Joined: 18 Dec 2016
Posts: 18
Location: United Kingdom
GMAT 1: 690 Q47 V38 GPA: 4
WE: Investment Banking (Investment Banking)
Re: A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre  [#permalink]

Show Tags

Thanks a lot
Makes sense, just thought it the wrong way around

Sent from my InFocus M808 using GMAT Club Forum mobile app
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre  [#permalink]

Show Tags

HarveyKlaus wrote:
A bag contains 3 blue disks, 3 green disks and 4 orange disks. If three disks are selected random from the bag, what is the probability that 1 of the disks will be green and the other 2 of the disks will be orange?

A) 1/30
B) 1/20
C) 3/40
D) 1/10
E) 3/20

We are given that in a bag there are 3 blue disks, 3 green disks, and 4 orange disks. We need to determine the probability that from 3 selected disks, 1 will be green and 2 will be orange.

Let’s first determine the total number of ways to select 1 green disk from 3.

3C1 = 3

Next, let’s determine the number of ways to select 2 orange disks from 4.

4C2 = (4 x 3)/2! = (4 x 3)/(2 x 1) = 6 ways

So, there are 3 x 6 = 18 ways to select 1 green and 2 orange disks.

Now let’s determine the number of ways to select 3 disks from 10:

10C3 = (10 x 9 x 8)/3! = (10 x 9 x 8)/(3 x 2) = 5 x 3 x 8 = 120

Thus, the probability of selecting 1 green disk and 2 orange disks is 18/120 = 3/20.

Alternate Solution:

Selecting 3 disks at once is equivalent to selecting them one at a time without replacement. Remember, we are determining the probability of selecting 1 green disk and 2 orange disks from 10 total disks.

If we select the green disk first, since there are 3 green disks and 10 total disks, there is a 3/10 chance that the green disk will be selected. Next, since there are 4 orange disks and 9 disks left, there is a 4/9 chance an orange disk will be selected. Similarly, for the third disk chosen, there is a 3/8 chance another orange disk will be selected. However, there are 3 different ways to select the 1 green disk and 2 orange disks:

G - O - O

O - G - O

O - O - G

Each of these 3 ways has the same probability of occurring. Thus, the total probability is:

3 x (3/10 x 4/9 x 3/8) = 3/20

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 13262
Re: A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre  [#permalink]

Show Tags

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: A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre   [#permalink] 09 Apr 2018, 19:41
Display posts from previous: Sort by

A bag contains 3 blue disks, 3 green disks and 4 orange disks. If thre

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

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