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.
Probability
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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
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