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Probability

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by SigGolfer » Tue Aug 21, 2007 5:26 am
I just want to make sure that I understand this concept correctly. Please let me know if the following is correct.

There are 3 green balls and 5 red balls in a bag.

The probability of choosing a ball of one color, then a ball of another color would be 3/8 x 5/7 = 15/56 (around 25%)

The probability of choosing two red balls would be 5/8 x 4/7 = 20/56 (around 35%)

The probability of choosing two green balls would be 3/8 x 2/7 = 6/56 (around 11%)

Is this correct? Thanks, I'm just trying to get the basics down.
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Source: — Quantitative Reasoning |
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by erdnah » Tue Aug 21, 2007 5:31 am
I think the probability of choosing a ball of one color, then a ball of another color would be 3/8 x 5/7 + 5/8 x 3/7 = 15/56 + 15/56 = 30/56 = 15/28.

This seems right, since it is the counterpart of the two other possibilities:
two red balls would be 5/8 x 4/7 = 20/56 (around 35%)
+ two green balls would be 3/8 x 2/7 = 6/56 (around 11%)
+ probability of choosing a ball of one color, then a ball of another = 30/56
= 56/56 = 1
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by SigGolfer » Tue Aug 21, 2007 5:43 am
Thanks for your response. That's what I meant.

First red, then green 15/56
First green, then red 15/56

Either red or green, then the opposite color 30/56.
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