Brent thats very helpful!
We would like to see some more questions(If you can post) for advanced level practice.
Thanks!
Probability - 10 marbles
-
winniethepooh
- Master | Next Rank: 500 Posts
- Posts: 370
- Joined: Sat Jun 11, 2011 8:50 pm
- Location: Arlington, MA.
- Thanked: 27 times
- Followed by:2 members
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Hi AbhiJ,AbhiJ wrote:There is an assumption in this problem that all the same colored marbles are identical. If they are different then the answer would be 2/(!10)
The answer is still 1/126 even if we say that the 10 balls are unique.
Please see my comments from "Mon Jul 25, 2011 7:42am" in this thread (on page 2, in response to winniethepooh's question)
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
abhisays
- Senior | Next Rank: 100 Posts
- Posts: 54
- Joined: Sun Nov 29, 2009 7:11 pm
- Location: Bangalore
- Thanked: 4 times
The answer is A
Here comes the solution ::
probability = no. of favorable cases/ total no. of cases.
the total number of cases will be (10*9*8*7*6*5*4*3*2*1) = 10!
logic is... first ball can be selected in 10 ways second in 9 and so on.
favorable no. of cases = 5!5! + 5!5! = 2*5!5!
logic is.. here only same color of marble will go to girls..
so the answer will be 2*5!5!/10!
Here comes the solution ::
probability = no. of favorable cases/ total no. of cases.
the total number of cases will be (10*9*8*7*6*5*4*3*2*1) = 10!
logic is... first ball can be selected in 10 ways second in 9 and so on.
favorable no. of cases = 5!5! + 5!5! = 2*5!5!
logic is.. here only same color of marble will go to girls..
so the answer will be 2*5!5!/10!
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Another great solution where we treat each marble as unique and then apply counting techniques.abhisays wrote:The answer is A
Here comes the solution ::
probability = no. of favorable cases/ total no. of cases.
the total number of cases will be (10*9*8*7*6*5*4*3*2*1) = 10!
logic is... first ball can be selected in 10 ways second in 9 and so on.
favorable no. of cases = 5!5! + 5!5! = 2*5!5!
logic is.. here only same color of marble will go to girls..
so the answer will be 2*5!5!/10!
These solutions illustrate all of the different options one has when tackling probability questions.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
olegpoi
- Senior | Next Rank: 100 Posts
- Posts: 31
- Joined: Thu Aug 12, 2010 12:40 am
- Thanked: 1 times
- Followed by:1 members
A 1/126
Could not find the comment to afore mentioned solution, which helped me solve the question.
Here are two scenarios:
1. Each of the Girls select black marble
5/10x4/9x3/8x2/7x1/6
or
2. Each of the Girls select white marble
5/10x4/9x3/8x2/7x1/6
Adding scenarios: 2x5!/10x9x8x7x6=1/126
Is this a correct approach?
Thanks.
Could not find the comment to afore mentioned solution, which helped me solve the question.
Here are two scenarios:
1. Each of the Girls select black marble
5/10x4/9x3/8x2/7x1/6
or
2. Each of the Girls select white marble
5/10x4/9x3/8x2/7x1/6
Adding scenarios: 2x5!/10x9x8x7x6=1/126
Is this a correct approach?
Thanks.
I thought the likelihood of 5 girls picking the same colored marbles was pretty slim to start. After looking at the answer choices I thought it highly unlikely that choices C D or E were correct. That left A and B. I then did 10*9*8*7*6/5*4*3*2*1. That gave me 252. Since that wasn't one of the choices I divided it by 2 figuring 5 was half of 10 and low and behold it's 126. 1/126 was a choice. Bingo. Not so pretty but at this point in my studying, that's how I'd have done it on the exam.
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Awesome solution, siebecker! I even think it is "pretty."siebecker wrote:I thought the likelihood of 5 girls picking the same colored marbles was pretty slim to start. After looking at the answer choices I thought it highly unlikely that choices C D or E were correct. That left A and B. I then did 10*9*8*7*6/5*4*3*2*1. That gave me 252. Since that wasn't one of the choices I divided it by 2 figuring 5 was half of 10 and low and behold it's 126. 1/126 was a choice. Bingo. Not so pretty but at this point in my studying, that's how I'd have done it on the exam.
The great thing about probability questions is that we all have an innate feeling for the likelihood of an event.
With a gut feeling alone, we can eliminate 3 answer choices (C, D and E), leaving us with a 50-50 shot. Pretty good odds since it took only 10-15 seconds to get to that point.
If I were running short on time, I might pick A or B and spend my time on a different question.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
Himanshu Vyas
- Newbie | Next Rank: 10 Posts
- Posts: 2
- Joined: Mon Jul 25, 2011 1:26 am
I also got "A"..Here is the simplest approach:
Prob = Favorable/Total
Now, Total i.e. Choosing 10 marbles out of 10 without replacement(meaning Permutation)=10P10 =10!
And, Favorable i.e. {(5 girls choose 5 whites without replacement) AND( 5 boys choose 5 blacks without replacement )} OR {(five girls choose 5 blacks without replacement)AND (five boys choose 5 whites without replacement)} = 5P5 x 5P5 + 5P5 x 5P5 = 2x (5P5x 5P5)= 2x5!x5! (Analogy--> AND is "x" , OR is "+")
Therefore, Prob = 2x5!x5!/10! = 1/126 (Ans)
Hi BRENT: Please let me know your feedback on this approach!!
Prob = Favorable/Total
Now, Total i.e. Choosing 10 marbles out of 10 without replacement(meaning Permutation)=10P10 =10!
And, Favorable i.e. {(5 girls choose 5 whites without replacement) AND( 5 boys choose 5 blacks without replacement )} OR {(five girls choose 5 blacks without replacement)AND (five boys choose 5 whites without replacement)} = 5P5 x 5P5 + 5P5 x 5P5 = 2x (5P5x 5P5)= 2x5!x5! (Analogy--> AND is "x" , OR is "+")
Therefore, Prob = 2x5!x5!/10! = 1/126 (Ans)
Hi BRENT: Please let me know your feedback on this approach!!
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Hi Himanshu Vyas,Himanshu Vyas wrote:I also got "A"..Here is the simplest approach:
Prob = Favorable/Total
Now, Total i.e. Choosing 10 marbles out of 10 without replacement(meaning Permutation)=10P10 =10!
And, Favorable i.e. {(5 girls choose 5 whites without replacement) AND( 5 boys choose 5 blacks without replacement )} OR {(five girls choose 5 blacks without replacement)AND (five boys choose 5 whites without replacement)} = 5P5 x 5P5 + 5P5 x 5P5 = 2x (5P5x 5P5)= 2x5!x5! (Analogy--> AND is "x" , OR is "+")
Therefore, Prob = 2x5!x5!/10! = 1/126 (Ans)
Hi BRENT: Please let me know your feedback on this approach!!
Your approach is perfect - nice work!
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Doesn't the order of selection change the conditional probabilities? Do the boys go first? Do the boys and girls take turns picking their marbles?Brent@GMATPrepNow wrote:The answer is, indeed, A (1/126)
Here's my solution:
The easiest/fastest way to determine the probability is to examine the probability of each necessary outcome to guarantee that the girls (and subsequently the boys) draw the same colored marble.
We get [P(1st girl selects any marble) x P(2nd girl selects marble the same color as 1st girl) x P(3nd girl selects marble the same color as 1st girl) x P(4th girl selects marble the same color as 1st girl) x P(5th girl selects marble the same color as 1st girl) x P(boys getting same color ball from remaining balls)
This equals: 1 x 4/9 x 3/8 x 2/7 x 1/6 x 1
Which equals: 1/126
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Great questions.edge wrote: Doesn't the order of selection change the conditional probabilities? Do the boys go first? Do the boys and girls take turns picking their marbles?
Do the boys go first?
If the boys go first, the calculations are the same, since P(girls get the same color) is exactly the same as P(boys get the same color)
Do the boys and girls take turns picking their marbles?
Let's alternate the selections (G-B-G-B-...).
So, P(girls get the same color)= P(girl1 picks any color AND boy1 picks different color AND girl2 picks same color as girl1 AND boy2 picks same color as boy1 AND . . . )
Applying the AND probability rule, we get:
P(girls get the same color)= P(girl1 picks any color) x P(boy1 picks different color) x P(girl2 picks same color as girl1) x P(boy2 picks same color as boy1) x . . .
Now we'll find each probability to get:
P(girls get the same color)= 1 x 5/9 x 4/8 x 4/7 x 3/6 x 3/5 x 2/4 x 2/3 x 1/2 x 1
= 1/126
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
Deependra1
- Senior | Next Rank: 100 Posts
- Posts: 53
- Joined: Sun Apr 10, 2011 12:15 pm
- Thanked: 1 times
-
Deependra1
- Senior | Next Rank: 100 Posts
- Posts: 53
- Joined: Sun Apr 10, 2011 12:15 pm
- Thanked: 1 times
I realised my folly .... made the classic mistake and fell into the trap.
Brent .... Thanks for the solution.
Brent .... Thanks for the solution.
