Comments on: Fun with probability and combinatorics on the GMAT http://www.knewton.com/blog/gmat/2010/02/01/fun-with-probability-and-combinatorics-on-the-gmat/ Tue, 15 May 2012 19:08:00 +0000 hourly 1 http://wordpress.org/?v=3.3.2 By: EvaJager http://www.knewton.com/blog/gmat/2010/02/01/fun-with-probability-and-combinatorics-on-the-gmat/#comment-1158 EvaJager Wed, 11 May 2011 22:35:00 +0000 http://www.knewtonblog.com/?p=1923#comment-1158 Another idea: rephrase the question. There are two Red balls (Jim and John) and 4 Black balls (the other people). What is the probability to draw two Red balls (exactly the pair Jim and John) if two randomly balls are chosen without return? Then the anser is really simple: 2/6x1/5=1/15. The probability is 2/6 to draw the first Red ball, after that, 1/5 to draw the second Red. Another idea: rephrase the question. There are two Red balls (Jim and John) and 4 Black balls (the other people). What is the probability to draw two Red balls (exactly the pair Jim and John) if two randomly balls are chosen without return?
Then the anser is really simple: 2/6×1/5=1/15. The probability is 2/6 to draw the first Red ball, after that, 1/5 to draw the second Red.

]]> By: EvaJager http://www.knewton.com/blog/gmat/2010/02/01/fun-with-probability-and-combinatorics-on-the-gmat/#comment-2483 EvaJager Wed, 11 May 2011 22:35:00 +0000 http://www.knewtonblog.com/?p=1923#comment-2483 Another idea: rephrase the question. There are two Red balls (Jim and John) and 4 Black balls (the other people). What is the probability to draw two Red balls (exactly the pair Jim and John) if two randomly balls are chosen without return? Then the anser is really simple: 2/6x1/5=1/15. The probability is 2/6 to draw the first Red ball, after that, 1/5 to draw the second Red. Another idea: rephrase the question. There are two Red balls (Jim and John) and 4 Black balls (the other people). What is the probability to draw two Red balls (exactly the pair Jim and John) if two randomly balls are chosen without return?
Then the anser is really simple: 2/6×1/5=1/15. The probability is 2/6 to draw the first Red ball, after that, 1/5 to draw the second Red.

]]> By: Evajager http://www.knewton.com/blog/gmat/2010/02/01/fun-with-probability-and-combinatorics-on-the-gmat/#comment-1157 Evajager Mon, 09 May 2011 20:48:00 +0000 http://www.knewtonblog.com/?p=1923#comment-1157 Well, if I would try to explain it to a layman, I would make it really simple. 1) Define probability - the ratio between the number of "desired" outcomes and the total number of possible outcomes. "Desired" outcomes - how many couples including Jim and John can be selected, all possible outcomes - the total number of couples that can be selected from the 6 workers. 2) If we take into account the order in which people were chosen, than there are 2 "desired" couples (John,Jim), (Jim,John). The total number of possible chosen couples is 6x5 (as there are 6 possibilities to chose the first person and 5 to chose the second one). So, the probability is 2/30=1/15. 3) If the order in which people were chosen does not matter, than there is just one "desired" couple, consisting of Jim and John. The total number of possible chosen couples is 6x5/2=15, because 6x5=30 represents each couple counted twice, like (a,b) and (b,a). Therefore, the probability is again 1/15. I think for many probability and combinatorics question on GMAT, one can do pretty well by sticking to straightforward reasoning, without the factorial formulas. But don't forget to pay attention when considering choices with or without order, and use the basic probability definition correctly. Well, if I would try to explain it to a layman, I would make it really simple.
1) Define probability – the ratio between the number of “desired” outcomes and the total number of possible outcomes. “Desired” outcomes – how many couples including Jim and John can be selected, all possible outcomes – the total number of couples that can be selected from the 6 workers.
2) If we take into account the order in which people were chosen, than there are 2 “desired” couples (John,Jim), (Jim,John). The total number of possible chosen couples is 6×5 (as there are 6 possibilities to chose the first person and 5 to chose the second one). So, the probability is 2/30=1/15.
3) If the order in which people were chosen does not matter, than there is just one “desired” couple, consisting of Jim and John. The total number of possible chosen couples is 6×5/2=15, because 6×5=30 represents each couple counted twice, like (a,b) and (b,a). Therefore, the probability is again 1/15.

I think for many probability and combinatorics question on GMAT, one can do pretty well by sticking to straightforward reasoning, without the factorial formulas. But don’t forget to pay attention when considering choices with or without order, and use the basic probability definition correctly.

]]> By: Evajager http://www.knewton.com/blog/gmat/2010/02/01/fun-with-probability-and-combinatorics-on-the-gmat/#comment-2474 Evajager Mon, 09 May 2011 20:48:00 +0000 http://www.knewtonblog.com/?p=1923#comment-2474 Well, if I would try to explain it to a layman, I would make it really simple. 1) Define probability - the ratio between the number of "desired" outcomes and the total number of possible outcomes. "Desired" outcomes - how many couples including Jim and John can be selected, all possible outcomes - the total number of couples that can be selected from the 6 workers. 2) If we take into account the order in which people were chosen, than there are 2 "desired" couples (John,Jim), (Jim,John). The total number of possible chosen couples is 6x5 (as there are 6 possibilities to chose the first person and 5 to chose the second one). So, the probability is 2/30=1/15. 3) If the order in which people were chosen does not matter, than there is just one "desired" couple, consisting of Jim and John. The total number of possible chosen couples is 6x5/2=15, because 6x5=30 represents each couple counted twice, like (a,b) and (b,a). Therefore, the probability is again 1/15. I think for many probability and combinatorics question on GMAT, one can do pretty well by sticking to straightforward reasoning, without the factorial formulas. But don't forget to pay attention when considering choices with or without order, and use the basic probability definition correctly. Well, if I would try to explain it to a layman, I would make it really simple.
1) Define probability – the ratio between the number of “desired” outcomes and the total number of possible outcomes. “Desired” outcomes – how many couples including Jim and John can be selected, all possible outcomes – the total number of couples that can be selected from the 6 workers.
2) If we take into account the order in which people were chosen, than there are 2 “desired” couples (John,Jim), (Jim,John). The total number of possible chosen couples is 6×5 (as there are 6 possibilities to chose the first person and 5 to chose the second one). So, the probability is 2/30=1/15.
3) If the order in which people were chosen does not matter, than there is just one “desired” couple, consisting of Jim and John. The total number of possible chosen couples is 6×5/2=15, because 6×5=30 represents each couple counted twice, like (a,b) and (b,a). Therefore, the probability is again 1/15.

I think for many probability and combinatorics question on GMAT, one can do pretty well by sticking to straightforward reasoning, without the factorial formulas. But don’t forget to pay attention when considering choices with or without order, and use the basic probability definition correctly.

]]> By: Andrew Zwelling http://www.knewton.com/blog/gmat/2010/02/01/fun-with-probability-and-combinatorics-on-the-gmat/#comment-1156 Andrew Zwelling Tue, 02 Feb 2010 16:19:17 +0000 http://www.knewtonblog.com/?p=1923#comment-1156 I love this blog. Now you need a twitter account I love this blog. Now you need a twitter account

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