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. ]]>

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. ]]>

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.

]]>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.

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