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:

In a department store prize box, 40% of the notes give... [#permalink]

Show Tags

18 Sep 2013, 12:31

1

This post received KUDOS

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

64% (03:06) correct
36% (02:16) wrong based on 114 sessions

HideShow timer Statistics

In a department store prize box, 40% of the notes give the winner a dreamy vacation; the other notes are blank. What is the approximate probability that 3 out of 5 people that draw the notes one after the other, and immediately return their note into the box get a dreamy vacation?

In a department store prize box, 40% of the notes give the winner a dreamy vacation; the other notes are blank. What is the approximate probability that 3 out of 5 people that draw the notes one after the other, and immediately return their note into the box get a dreamy vacation?

a) 0.12 b) 0.23 c) 0.35 d) 0.45 e) 0.65

The probability of winning is 40% = 40/100 = 2/5. The probability of NOT winning is 60% = 3/5.

\(P(WWWNN)=\frac{5!}{3!2!}*(\frac{2}{5})^3*(\frac{3}{5})^2=\frac{144}{625}\approx{23}\) (we multiply by \(\frac{5!}{3!2!}\), because WWWNN scenario can occur in several ways: WWWNN, WWNWN, WNWWN, NWWWN, ... the # of such cases basically equals to the # of permutations of 5 letters WWWNN, which is \(\frac{5!}{3!2!}\)).

Re: In a department store prize box, 40% of the notes give... [#permalink]

Show Tags

21 Nov 2014, 11:04

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.
_________________

How it was solved above is from a formula specifically for the probability when x will occur and when not x will occur, the Bernoulli formula. The initial part of your expression selects three out of five people correctly. However, the second part of the expression is essentially the same thing except for the probability for not x, which is an equally important part as anything else. Thus, extend the expression with the probability of not x:

Re: In a department store prize box, 40% of the notes give... [#permalink]

Show Tags

20 Dec 2015, 18:24

ok, first, I did not how to tackle this question... so we we need to have 3 winners out of 5. this can be done in 5C3 ways, or 10 ways. WWWLL LWWWL LLWWW etc. so 10 ways.

now, the probability of winning is 4/10, and probability of loosing is 6/10 i did not simplify, since working with 10's are much easier.

so 4/10 must be 3 times, and 6/10 twice. (4/10)^3*(6/10)^2 * 10 (10 ways we can arrange winners and losers). ok, so (4/10)^3 = 64/1000 (6/10)^2 = 36/100 now, the first one can be multiplied by 10, and rewritten as 64/100 now, multiply 64/100 with 36/100. this will be equal to 2304/10000 this is aprox. 23/100 or 0.23

Re: In a department store prize box, 40% of the notes give... [#permalink]

Show Tags

22 Dec 2015, 12:43

Quote:

The probability of winning is 40% = 40/100 = 2/5. The probability of NOT winning is 60% = 3/5.

P(WWWNN)=5!3!2!∗(25)3∗(35)2=144625≈23 (we multiply by 5!3!2!, because WWWNN scenario can occur in several ways: WWWNN, WWNWN, WNWWN, NWWWN, ... the # of such cases basically equals to the # of permutations of 5 letters WWWNN, which is 5!3!2!).

Answer: B.

Why do we have to divide by 3!2!? I thought that simply multiply it by 5! as it is permutation.

Re: In a department store prize box, 40% of the notes give... [#permalink]

Show Tags

22 Dec 2015, 12:47

1

This post received KUDOS

zurich wrote:

Quote:

The probability of winning is 40% = 40/100 = 2/5. The probability of NOT winning is 60% = 3/5.

P(WWWNN)=5!3!2!∗(25)3∗(35)2=144625≈23 (we multiply by 5!3!2!, because WWWNN scenario can occur in several ways: WWWNN, WWNWN, WNWWN, NWWWN, ... the # of such cases basically equals to the # of permutations of 5 letters WWWNN, which is 5!3!2!).

Answer: B.

Why do we have to divide by 3!2!? I thought that simply multiply it by 5! as it is permutation.

because 3 winners can be arranged in different orders, and it doesn't matter how they are arranged. it might be W1W2W3 or W2W1W3 -> note that winner is a winner, and they are all the same. because of this, we have to divide by 3! since we have 2 non-winners, those one can be arranged as well in 2! ways, since we do not distinguish between L1 and L2.

Re: In a department store prize box, 40% of the notes give... [#permalink]

Show Tags

30 Dec 2015, 11:21

1

This post received KUDOS

zurich wrote:

Quote:

The probability of winning is 40% = 40/100 = 2/5. The probability of NOT winning is 60% = 3/5.

P(WWWNN)=5!3!2!∗(25)3∗(35)2=144625≈23 (we multiply by 5!3!2!, because WWWNN scenario can occur in several ways: WWWNN, WWNWN, WNWWN, NWWWN, ... the # of such cases basically equals to the # of permutations of 5 letters WWWNN, which is 5!3!2!).

Answer: B.

Why do we have to divide by 3!2!? I thought that simply multiply it by 5! as it is permutation.

Hi Zurich,

In this case the order of the people selecting the notes does not matter. It can be looked at as a combination, instead of a permutation. The number of ways to select 3 winners out of 5 is given by 5C3 = \(\frac{5!}{3!2!}\)

It is mathematically the same as saying we will find the number of permutations of 5 people, but when there are 3 identical and 2 identical people in the group. In this case, we must divide the permutation of 5 people, 5!, by the number of arrangements of each of the identical elements, 3! and 2!.

This again equals \(\frac{5!}{3!2!}\)

The only difference is the way we explain it. Either we are choosing 3 out of 5 where the order doesn't matter, or we are arranging 3 identical and 2 identical items in a row. It works out to the same thing.

I hope that helps to clear it up!
_________________

Dave de Koos GMAT aficionado

gmatclubot

Re: In a department store prize box, 40% of the notes give...
[#permalink]
30 Dec 2015, 11:21

Hey, guys, So, I’ve decided to run a contest in hopes of getting the word about the site out to as many applicants as possible this application season...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...