Author 
Message 
TAGS:

Hide Tags

Intern
Affiliations: AIESEC
Joined: 13 Feb 2011
Posts: 2
Smit: K

A box contains 100 balls, numbered from 1 to 100. If three b [#permalink]
Show Tags
13 Feb 2011, 11:46
6
This post received KUDOS
35
This post was BOOKMARKED
Question Stats:
55% (02:08) correct
45% (01:22) wrong based on 560 sessions
HideShow timer Statistics
A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd? A. 1/4 B. 3/8 C. 1/2 D. 5/8 E. 3/4
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 28 May 2013, 15:54, edited 2 times in total.
Edited the question and added the OA



Math Expert
Joined: 02 Sep 2009
Posts: 39609

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
13 Feb 2011, 12:14
10
This post received KUDOS
Expert's post
11
This post was BOOKMARKED
SmitKhurana wrote: Hello there GMAT enthusiasts!
Surely this finds everyone in great guns towards achieving a perfect GMAT Score, in between came across this very peculiar and relatively difficult question for resolution :
Q. A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the 3 numbers on the balls selected from the box will be odd ? Welcome to GMAT Club! Please read and follow: howtoimprovetheforumsearchfunctionforothers99451.html So please: Provide answer choices for PS questions.Original question is: A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?A. 1/4 B. 3/8 C. 1/2 D. 5/8 E. 3/4 The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd); P(OOO)=(1/2)^3; P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE); So finally P=1/8+3/8=1/2. Answer: C. Alternately you can notice that since there are equal chances to get even or odd sum after two selections (for even sum it's EE or OO and for odd sum it's EO or OE) then there is 1/2 chances the third ball to make the sum odd.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 21 Mar 2010
Posts: 310

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
14 Feb 2011, 12:47
1
This post received KUDOS
What is the official answer.
Since replacement is involved, i would think the order of the EEO ball being picked does not matter.
Thus P(E)&P(E)&P(O) should be 1/8
1/8+1/8 = 1/4.



Math Expert
Joined: 02 Sep 2009
Posts: 39609

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
14 Feb 2011, 12:56
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED



Senior Manager
Joined: 21 Mar 2010
Posts: 310

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
14 Feb 2011, 13:26
The order will matter if there is no replacement:
If the first pick is even, the probability of a second even will be 49/99 and odd will be 50/99.
Also, im looking at these as mutually independent events rather than Probability of EEO +EOE etc.
But if i write out all the possibilities
ooo ooe oeo oee eoo eoe eeo eee
then i can see that 4 out of 8 picks are favorable.
This one is tricky!



Math Expert
Joined: 02 Sep 2009
Posts: 39609

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
14 Feb 2011, 13:31
mbafall2011 wrote: The order will matter if there is no replacement:
If the first pick is even, the probability of a second even will be 49/99 and odd will be 50/99.
Also, im looking at these as mutually independent events rather than Probability of EEO +EOE etc.
But if i write out all the possibilities
ooo ooe oeo oee eoo eoe eeo eee
then i can see that 4 out of 8 picks are favorable.
This one is tricky! Again order does matter. P(odd sum)=P(EEO)+P(EOE)+P(OEE)+P(OOO)=1/8+1/8+1/8+1/8=1/2. Next, the way you are doing (the red part) is correct only for the cases in which there are equal # of even and odd numbers (for example if there were balls numbered from 1 to 99 this approach wouldn't be corrorect, so after all the probability approach is better).
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 08 Nov 2010
Posts: 408
WE 1: Business Development

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
16 Feb 2011, 00:43
1
This post received KUDOS
Bunuel  can you please do this one If it was without replacement? so ill be sure i understood it the right way? thanks.
_________________
GMAT Club Premium Membership  big benefits and savings



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
16 Feb 2011, 01:09
1
This post received KUDOS
144144 wrote: Bunuel  can you please do this one If it was without replacement?
so ill be sure i understood it the right way?
thanks. Without replacement; the condition for getting odd doesn't change; only the probability of picking up the ball does; OEE EOE EEO OOO 50/100*50/99*49/98+50/100*50/99*49/98+50/100*49/99*50/98+50/100*49/99*48/98 =1/2*50/99*1/2+1/2*50/99*1/2+1/2*49/99*25/49+1/2*49/99*24/49 rest can be simplified. Correct me if I am wrong, Bunuel.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 39609

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
16 Feb 2011, 03:48
7
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
fluke wrote: 144144 wrote: Bunuel  can you please do this one If it was without replacement?
so ill be sure i understood it the right way?
thanks. Without replacement; the condition for getting odd doesn't change; only the probability of picking up the ball does; OEE EOE EEO OOO 50/100*50/99*49/98+50/100*50/99*49/98+50/100*49/99*50/98+50/100*49/99*48/98 =1/2*50/99*1/2+1/2*50/99*1/2+1/2*49/99*25/49+1/2*49/99*24/49 rest can be simplified. Correct me if I am wrong, Bunuel. Odd sum: OEE EOE EEO OOOEven sum: EEE EOO OEO OOENow, no matter whether we have with or without replacement case, the probability of red events and the probability of blue events will be symmetrical and equal (because there are equal number of even and odd balls) and since the above events describe all possible outcomes when we pick 3 balls and are mutually exclusive then their sum must be 1: \(P(red)=P(blue)=\frac{1}{2}\). To demonstrate for without replacement case: \(P=3*\frac{50}{100}*\frac{50}{99}*\frac{49}{98}+\frac{50}{100}*\frac{49}{99}*\frac{48}{98}=\frac{3*50*49}{100*99*98}(50+16)=\frac{1}{2*33*2}*66=\frac{1}{2}\). Combinatorial approach for without replacement case: \(P=\frac{C^1_{50}*C^2_{50}+C^3_{50}}{C^3_{100}}=\frac{1}{2}\). Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 08 Nov 2010
Posts: 408
WE 1: Business Development

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
16 Feb 2011, 04:40
Bunuel  u r amazing.great explanation from all aspects. thanks. +1 +1 fluke
_________________
GMAT Club Premium Membership  big benefits and savings



Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 633

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
16 Feb 2011, 05:12



Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 533
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
17 Feb 2011, 11:55
Baten80 wrote: SmitKhurana wrote: Hello there GMAT enthusiasts!
Surely this finds everyone in great guns towards achieving a perfect GMAT Score, in between came across this very peculiar and relatively difficult question for resolution :
Q. A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the 3 numbers on the balls selected from the box will be odd ? Please give the link from which i can download the questionsYou have to purchase them from mba.com, However, if you're looking for Combinatorics/ probability questions, you can find them here: permutationscombinationsprobabilitydownloadquestions57156.html
_________________
My GMAT debrief: http://gmatclub.com/forum/from620to710mygmatjourney114437.html



Intern
Joined: 13 Feb 2012
Posts: 20
WE: Other (Transportation)

Re: A box contains 100 balls, numbered from 1 to 100. If three b [#permalink]
Show Tags
28 Mar 2012, 06:10
Can anyone answer my question? Since we have equal number of odd and even numbers (with replacement) isn't it selfexplanatory that the probability of the sum to be odd will be the same of that to be even = 1/2?? I thing that this approach can be applied at any case with replacement i.e. if we pick 4 or 5 or 6 or 50 etc balls the probability of their sum to be odd (even) will be 1/2. Because in this way the answer can be given in 10 seconds...



Intern
Joined: 28 Mar 2012
Posts: 12

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
28 Apr 2012, 06:57
Bunuel wrote: Again order does matter. P(odd sum)=P(EEO)+P(EOE)+P(OEE)+P(OOO)=1/8+1/8+1/8+1/8=1/2. Excuse me, but I didn't understand why order does matter? At the end we are looking for the sum of the selected balls and not for the order of the selection, so whether it is 2+2+1 or 1+2+2 or 2+2+1 they are all the same! They all equal 4 which is one possible outcome and not 3



Math Expert
Joined: 02 Sep 2009
Posts: 39609

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
29 Apr 2012, 06:11



Intern
Joined: 02 Oct 2013
Posts: 12

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
27 Oct 2013, 06:45
Bunuel wrote: SmitKhurana wrote: Hello there GMAT enthusiasts!
Surely this finds everyone in great guns towards achieving a perfect GMAT Score, in between came across this very peculiar and relatively difficult question for resolution :
Q. A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the 3 numbers on the balls selected from the box will be odd ? Welcome to GMAT Club! Please read and follow: howtoimprovetheforumsearchfunctionforothers99451.html So please: Provide answer choices for PS questions.Original question is: A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?A. 1/4 B. 3/8 C. 1/2 D. 5/8 E. 3/4 The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd); P(OOO)=(1/2)^3; P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE); So finally P=1/8+3/8=1/2. Answer: C. Alternately you can notice that since there are equal chances to get even or odd sum after two selections (for even sum it's EE or OO and for odd sum it's EO or OE) then there is 1/2 chances the third ball to make the sum odd. Hi Bunuel Can you explain this in terms of favourable / Total Regards



Intern
Joined: 27 Oct 2013
Posts: 4

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
28 Oct 2013, 00:02
Bunuel wrote: Mochad wrote: Bunuel wrote: Again order does matter. P(odd sum)=P(EEO)+P(EOE)+P(OEE)+P(OOO)=1/8+1/8+1/8+1/8=1/2. Excuse me, but I didn't understand why order does matter? At the end we are looking for the sum of the selected balls and not for the order of the selection, so whether it is 2+2+1 or 1+2+2 or 2+2+1 they are all the same! They all equal 4 which is one possible outcome and not 3Consider below two scenarios: First=Even, Second=Even, Third=Odd; First=Even, Second=Odd, Third=Even; Are these scenarios the same? No. That's why the order matters. Argh... it depends on how you look at the problem. If you calculate your full set of events where the order matters, then the order matters also for the "favorable" set of events. I treated the question where order doesn't matter (because it doesn't matter for summation and because we are allowed to disregard it since the balls are replaceable) and only looked at the end result of the number of balls I had after the selection process was over: 3x Odds 2x Odds + 1x Even 2x Evens + 1x Odd 3x Evens 2 of those are "favorable" (first and third), thus 2/4 = 1/2



Math Expert
Joined: 02 Sep 2009
Posts: 39609

Re: Question from the Official GMAC's GMAT Prep Question Bank [#permalink]
Show Tags
28 Oct 2013, 00:16
garazhaka wrote: Bunuel wrote: Mochad wrote: Consider below two scenarios: First=Even, Second=Even, Third=Odd; First=Even, Second=Odd, Third=Even;
Are these scenarios the same? No. That's why the order matters.
Argh... it depends on how you look at the problem. If you calculate your full set of events where the order matters, then the order matters also for the "favorable" set of events. I treated the question where order doesn't matter (because it doesn't matter for summation and because we are allowed to disregard it since the balls are replaceable) and only looked at the end result of the number of balls I had after the selection process was over: 3x Odds 2x Odds + 1x Even 2x Evens + 1x Odd 3x Evens 2 of those are "favorable" (first and third), thus 2/4 = 1/2 You get the probability of 1/2 in either case. But in this problem the order does matter. For example, the case of EEO is different from EOE.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 10 Mar 2013
Posts: 278
GMAT 1: 620 Q44 V31 GMAT 2: 690 Q47 V37 GMAT 3: 610 Q47 V28 GMAT 4: 700 Q50 V34 GMAT 5: 700 Q49 V36 GMAT 6: 690 Q48 V35 GMAT 7: 750 Q49 V42 GMAT 8: 730 Q50 V39

Re: A box contains 100 balls, numbered from 1 to 100. If three b [#permalink]
Show Tags
16 Aug 2014, 03:26
E = Even, O = Odd EEO = 1st ball is even, 2nd ball is even, 3rd ball is odd Prob(EEO) + Prob(EOE) + Prob(OEE) + Prob(OOO) = 4*Prob(EEO) = 4 * Prob(E)*Prob(E)*Prob(O) = 4*(1/2)^3 = 4/8 = 1/2



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15926

Re: A box contains 100 balls, numbered from 1 to 100. If three b [#permalink]
Show Tags
20 Aug 2015, 13:55
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A box contains 100 balls, numbered from 1 to 100. If three b
[#permalink]
20 Aug 2015, 13:55



Go to page
1 2
Next
[ 31 posts ]




