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:

10 t-shirts are available to choose. 5 of them are printed, [#permalink]

Show Tags

20 Jun 2004, 09:00

2

This post received KUDOS

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

93% (02:30) correct
7% (02:37) wrong based on 55 sessions

HideShow timer Statistics

10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

Please explain the steps (procedure)
_________________

10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

Please explain the steps (procedure)

1. Probability of at least 1 being a printed = 1 - P(none of them is printed).

10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

Please explain the steps (procedure)

You have 10 t-shirts. You need to choose 3 of them. You can do this in 10C3 = 10*9*8/3*2*1 = 120 ways.

You have 5 plain t-shirts. You can choose 3 out of them in 5C3 = 5*4/2 = 10 ways.

So you have total 120 ways of picking 3 t-shirts out of 10. In 10 of those ways, you pick all plain t-shirts. So what happens in the rest of the 110 ways? In those, you must be picking up at least one printed t-shirt.

So probability of picking at least one printed t-shirt = 110/120 = 11/12
_________________

Re: 10 t-shirts are available to choose. 5 of them are printed, [#permalink]

Show Tags

23 Sep 2015, 13:39

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: 10 t-shirts are available to choose. 5 of them are printed, [#permalink]

Show Tags

23 Sep 2015, 14:17

1

This post received KUDOS

carsen wrote:

10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

When it comes to probability questions involving "at least," it's best to try using the complement, as the above solutions have done. However, what if you didn't spot that shortcut? No problem, it will just take us a little bit longer.

P(at least 1 printed shirt) = (# of outcomes with at least 1 printed shirt)/(TOTAL # of possible outcomes)

Always start with the denominator.

TOTAL # of possible outcomes We have 10 shirts and we must select 3. Since the order in which we select the shirts doesn't matter, we can use combinations. We can select 3 shirts from 10 shirt in 10C3 ways (= 120 outcomes)

# of outcomes with at least 1 printed shirt We have 3 cases: Case 1: 1 printed shirt and 2 plain. So, select 1 of the 5 printed, and select 2 of the 5 plain. # of outcomes = (5C1)(5C2) = (5)(10) = 50 Case 2: 2 printed shirts and 1 plain. So, select 2 of the 5 printed, and select 1 of the 5 plain. # of outcomes = (5C2)(5C1) = (10)(5) = 50 Case 3: 3 printed shirts and 0 plain. So, select 3 of the 5 printed, and select 0 of the 5 plain. # of outcomes = (5C3)(5C0) = (10)(1) = 10

Re: 10 t-shirts are available to choose. 5 of them are printed, [#permalink]

Show Tags

25 Sep 2015, 08:58

VeritasPrepKarishma wrote:

carsen wrote:

10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

Please explain the steps (procedure)

You have 10 t-shirts. You need to choose 3 of them. You can do this in 10C3 = 10*9*8/3*2*1 = 120 ways.

You have 5 plain t-shirts. You can choose 3 out of them in 5C3 = 5*4/2 = 10 ways.

So you have total 120 ways of picking 3 t-shirts out of 10. In 10 of those ways, you pick all plain t-shirts. So what happens in the rest of the 110 ways? In those, you must be picking up at least one printed t-shirt.

So probability of picking at least one printed t-shirt = 110/120 = 11/12

Karishma,

This is the combinatorics approach if I am not wrong. Can you tell me how to solve this with probability approach. _________________

Freedom is not a gift...It is a responsibility to pass on.....

10 t-shirts are available to choose. 5 of them are printed, [#permalink]

Show Tags

27 Mar 2016, 02:37

Hi There,

Allow me to give u all the approach i did with this question

Firstly, there are 10 Shirts, which is 5 Printed (Pr) and 5 Plain (Pl)

and we need to find the probability for at least one of them 3 shirts is Printed (Pr)

and this can be done with the following event :

1 of 3 shirts is Pr (Pr Pl Pl) : there are 5C1 combination of this event or 2 of 3 shirts is Pr (Pr Pr Pl) : there are 5C2 combination of this event or all of the shirts is Pr (Pr Pr Pr) : there are 5C3 combination of this event

(please note that order does not matter so we can use Combination in here) (also notice the "or" above so that means we must use + (plus) for the total event)

and for the total probability of all shirts, there is total 3 shirts out of 10 we can use 10C3

So in the end we can calculate the probability with the following equation : (5C1 + 5C2 + 5C3) / 10C3 = 5/24

Re: 10 t-shirts are available to choose. 5 of them are printed, [#permalink]

Show Tags

27 Mar 2016, 06:52

VeritasPrepKarishma wrote:

carsen wrote:

10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

Please explain the steps (procedure)

You have 10 t-shirts. You need to choose 3 of them. You can do this in 10C3 = 10*9*8/3*2*1 = 120 ways.

You have 5 plain t-shirts. You can choose 3 out of them in 5C3 = 5*4/2 = 10 ways.

So you have total 120 ways of picking 3 t-shirts out of 10. In 10 of those ways, you pick all plain t-shirts. So what happens in the rest of the 110 ways? In those, you must be picking up at least one printed t-shirt.

So probability of picking at least one printed t-shirt = 110/120 = 11/12

Do we not need to consider the sequence in this - how do we decide?

10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

Please explain the steps (procedure)

You have 10 t-shirts. You need to choose 3 of them. You can do this in 10C3 = 10*9*8/3*2*1 = 120 ways.

You have 5 plain t-shirts. You can choose 3 out of them in 5C3 = 5*4/2 = 10 ways.

So you have total 120 ways of picking 3 t-shirts out of 10. In 10 of those ways, you pick all plain t-shirts. So what happens in the rest of the 110 ways? In those, you must be picking up at least one printed t-shirt.

So probability of picking at least one printed t-shirt = 110/120 = 11/12

Do we not need to consider the sequence in this - how do we decide?

No. Here you are just "selecting" 3 t-shirts. If you had to decide the sequence in which you could wear them over 3 days, then you would need to arrange them too. In this post, I have tried to explain the difference: http://www.veritasprep.com/blog/2016/01 ... mbination/ _________________

Re: 10 t-shirts are available to choose. 5 of them are printed, [#permalink]

Show Tags

09 Apr 2016, 02:01

carsen wrote:

10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

Please explain the steps (procedure)

probability of At least one is probability of (1 - none)

there are 5 non painted t-shirts that comes in 'none' category. choose 3 out of these 5.

Probability of at least one of them is a printed t-shirt = 1 - (5choose3/10choose3) = 1 - 1/12 = 11/12.
_________________

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...