Find all School-related info fast with the new School-Specific MBA Forum

It is currently 16 Sep 2014, 22:02

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A Bin contains card numbered from 1 to 20. If two cards are

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 27 May 2005
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

A Bin contains card numbered from 1 to 20. If two cards are [#permalink] New post 03 Jun 2005, 14:43
A Bin contains card numbered from 1 to 20. If two cards are drawn what is the probability the sum of the numbers on the cards is even ?


1/3
7/18
4/9
9/19
1/2

I think the answer should be 1/2 as opposed to 9/19 if am not wrong. For numbers 1-20, the sum of any 2 numbers is either even or odd, hence asked probability is 1/2

Can anyone point the flaw in the reasoning
thanks
Director
Director
avatar
Joined: 18 Feb 2005
Posts: 674
Followers: 1

Kudos [?]: 2 [0], given: 0

GMAT Tests User
Re: Probability Q in Challenge 17 [#permalink] New post 03 Jun 2005, 15:54
bmw wrote:
A Bin contains card numbered from 1 to 20. If two cards are drawn what is the probability the sum of the numbers on the cards is even ?


1/3
7/18
4/9
9/19
1/2

I think the answer should be 1/2 as opposed to 9/19 if am not wrong. For numbers 1-20, the sum of any 2 numbers is either even or odd, hence asked probability is 1/2

Can anyone point the flaw in the reasoning
thanks


It should be 9/19.

There are 10 even and 10 odd numbered cards

So to have the sum even either both of them should be even or both odd.

Even cases are same as odd cases

Lets take EVEN

there are 10 even numbers and you draw 2 out of them.

So first card is drawn in 10/20 ways and the second card in 9/19 ways

So the prob of drawing even card is 10*9/20*19

Same is the case with odd numbered cards

So total = 2*(10*9)/(20*19 ) = 9/19
Manager
Manager
avatar
Joined: 07 Mar 2005
Posts: 93
Followers: 1

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 03 Jun 2005, 16:20
I got 9/19 as well.

Approach:

How can a number be even?

Odd + odd and even + even

10/20 x 9/19 + 10/20 x 9/19

9/19
Director
Director
User avatar
Joined: 18 Apr 2005
Posts: 551
Location: Canuckland
Followers: 1

Kudos [?]: 7 [0], given: 0

GMAT Tests User
Re: Probability Q in Challenge 17 [#permalink] New post 03 Jun 2005, 17:41
bmw wrote:
A Bin contains card numbered from 1 to 20. If two cards are drawn what is the probability the sum of the numbers on the cards is even ?


1/3
7/18
4/9
9/19
1/2

I think the answer should be 1/2 as opposed to 9/19 if am not wrong. For numbers 1-20, the sum of any 2 numbers is either even or odd, hence asked probability is 1/2

Can anyone point the flaw in the reasoning
thanks


prob= (2*(10c2))/20c2 = 2*9*5/19*10 = 9/19

as far as the flaw in the reasoning is concerned

even if odd+odd or even+even, we have 10 odd numbers and 10 even numbers
so total even possiblities is 10c2 + 10c2 = 45 + 45 = 90

odd if odd + even, total 10*10 = 100 possibilities

check 20c2 = 19*10 = 190 possibilities overall

different counting concepts
Director
Director
avatar
Joined: 13 Nov 2003
Posts: 801
Location: BULGARIA
Followers: 1

Kudos [?]: 20 [0], given: 0

GMAT Tests User
 [#permalink] New post 03 Jun 2005, 23:33
We have 3 possible scenarios, the sum of O+E=O, E+E=E and O+O=E so the prob of the sum being even is 2/3
Senior Manager
Senior Manager
avatar
Joined: 17 Apr 2005
Posts: 377
Location: India
Followers: 1

Kudos [?]: 13 [0], given: 0

GMAT Tests User
Re: Probability Q in Challenge 17 [#permalink] New post 03 Jun 2005, 23:51
bmw wrote:
A Bin contains card numbered from 1 to 20. If two cards are drawn what is the probability the sum of the numbers on the cards is even ?


1/3
7/18
4/9
9/19
1/2

I think the answer should be 1/2 as opposed to 9/19 if am not wrong. For numbers 1-20, the sum of any 2 numbers is either even or odd, hence asked probability is 1/2

Can anyone point the flaw in the reasoning
thanks


I problem with your reasoning is that you pick both the numbers together and not one after the another, which is not bad, but you should conditional probability in that case , in the absence of which , it is akin to saying that the numbers can be replaced.

HMTG.
Senior Manager
Senior Manager
User avatar
Joined: 17 May 2005
Posts: 273
Location: Auckland, New Zealand
Followers: 1

Kudos [?]: 4 [0], given: 0

GMAT Tests User
Re: Probability Q in Challenge 17 [#permalink] New post 05 Jun 2005, 11:53
bmw wrote:
A Bin contains card numbered from 1 to 20. If two cards are drawn what is the probability the sum of the numbers on the cards is even ?


1/3
7/18
4/9
9/19
1/2

I think the answer should be 1/2 as opposed to 9/19 if am not wrong. For numbers 1-20, the sum of any 2 numbers is either even or odd, hence asked probability is 1/2

Can anyone point the flaw in the reasoning
thanks


If the first number is odd, second number has to be odd and if the first number is even, second number has to be even.

if you've already picked an odd number out of the box the prob of getting an odd one on the next go is 9/19 (as you have one less odd card in the box).

same thing if you pick an even number...

thus since the prob of picking an odd or even at the beginning is 1/2 and 1/2

the answer is 1/2* 9/19 + 1/2*9/19 = 9/19
SVP
SVP
User avatar
Joined: 03 Jan 2005
Posts: 2255
Followers: 12

Kudos [?]: 198 [0], given: 0

GMAT Tests User
Re: Probability Q in Challenge 17 [#permalink] New post 05 Jun 2005, 13:03
2C(10,2)/C(20,2)=2*10*9/20*19=9/19

Very curiously 9/19<1/2
It is because after you pick your first card, say it is odd, then it is a little less likely that your second draw will give you another odd, since there are more even cards then odd cards. So it is always less likely that you will draw two odd cards, or two even card, and it is more likely that you will draw one of each type.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Re: Probability Q in Challenge 17   [#permalink] 05 Jun 2005, 13:03
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic A deck of cards contains 6 cards numbered from 1 to 6. If Sepideh2612 15 08 Nov 2011, 01:26
The cards in a deck are numbered consecutively from 1 to 20. vanidhar 3 16 Oct 2010, 04:47
A bin contains 20 cards. If five cards are drawn without bmwhype2 2 07 Nov 2007, 08:03
A deck of cards contains 10 cards numbered from 1 to 10. kevincan 6 02 Aug 2006, 09:04
A deck of cards contains 6 cards numbered from 1 to 6. If GMATT73 4 01 Oct 2005, 21:35
Display posts from previous: Sort by

A Bin contains card numbered from 1 to 20. If two cards are

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.