Last visit was: 12 Dec 2024, 05:29 It is currently 12 Dec 2024, 05:29
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
avatar
araspai
avatar
Joined: 27 Jul 2003
Last visit: 24 Jan 2004
Posts: 93
Own Kudos:
184
Location: Singapore
Posts: 93
Kudos: 184
Bill's compact disc player randomly plays a song. If bill 20 Aug 2003, 05:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bill's compact disc player randomly plays a song. If bill plays a disc with 14 songs, What are the chances that the third song he hears will be his favorite?
a. 1/14 b. 1/12 c. 1/11 d. 3/14 e. 1/3



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
mciatto
User avatar
Joined: 10 Jun 2003
Last visit: 13 Jun 2005
Posts: 132
Own Kudos:
38
Location: Maryland
Posts: 132
Kudos: 38
Bill's compact disc player randomly plays a song. If bill 20 Aug 2003, 08:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
javropu
1/14?


That must be correct. In fact, the prob that ANY song he hears will be is favorite song is 1/14.
User avatar
bnagasub
User avatar
Joined: 19 Aug 2003
Last visit: 15 Sep 2003
Posts: 6
Own Kudos:
1
Location: Pittsburgh
Posts: 6
Kudos: 1
Bill's compact disc player randomly plays a song. If bill 20 Aug 2003, 22:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think the answer is B - 1/12.

The probability of any one song being his favourite is 1/14.

But in this case the CD player, randomly picks the songs. The probability of first song played being his favourite is 1/14. The second song played being his favourite is 1/13, as only 13 more are left after the first song has been played. Using the same logic, the third song played being his favourite is 1/12.

If the CD player is playing the songs serially (not random selection), what is the probability of 3rd song being his favourite?

1/14?!
User avatar
mciatto
User avatar
Joined: 10 Jun 2003
Last visit: 13 Jun 2005
Posts: 132
Own Kudos:
38
Location: Maryland
Posts: 132
Kudos: 38
Bill's compact disc player randomly plays a song. If bill 20 Aug 2003, 23:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If the CD player had already played two songs that were not his favorite, and the randomizer does not repeat songs until they have all been played, then your answer is correct - 1/12.
But as it stands, if the randomizer is random, then the odds are always 1/14.

With your logic, what are the odds that the 14th song played is his favorite? 1? Does that make sense?

What if he is on the airplane for 8 hrs. and the CD has been playing the whole time...what are the odds that the 60th song will be his favorite? By your logic, this would be negative!! And the correct answer is clearly 1/14.
User avatar
rshanm2
User avatar
Joined: 16 Aug 2003
Last visit: 01 Nov 2003
Posts: 4
Location: California
Posts: 4
Kudos: 0
Bill's compact disc player randomly plays a song. If bill 22 Aug 2003, 07:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is this the right way?

Total songs = 14
Not favorites = 13
Favorites = 1

P(Song 3 is favorite) = P(Song 1 not fav) * P(Song 2 not fav) * P(Song 3 fav)

= 13/14 * 12/13 * 1/12

= 1/14
User avatar
mciatto
User avatar
Joined: 10 Jun 2003
Last visit: 13 Jun 2005
Posts: 132
Own Kudos:
38
Location: Maryland
Posts: 132
Kudos: 38
Bill's compact disc player randomly plays a song. If bill 22 Aug 2003, 09:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rshanm2
Is this the right way?

Total songs = 14
Not favorites = 13
Favorites = 1

P(Song 3 is favorite) = P(Song 1 not fav) * P(Song 2 not fav) * P(Song 3 fav)

= 13/14 * 12/13 * 1/12

= 1/14


I would say that this is NOT the right way, but I could be wrong. Nowhere in the question does it say that the first two songs played are not his favorites. Thus the prob of this event is independant of any other event. But, your answer works, and in this case you would get the points.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3116 posts