<PRE><B>Question 1118158</B>
&lt;br&gt;
There are many ways to calculate probabilities like these.&lt;br&gt;
Basically, you want to put the worded requirements in terms of ANDs and/or ORs and then, in your calculations, replace each AND with a multiplication and each OR with an addition.&lt;br&gt;
You can count the number of ways of getting the desired outcome and get the probability by dividing by the total number of ways of choosing 2 of the 25 balls, which is C(25,2) = 300.&lt;br&gt;
Or you can think of drawing one ball at a time and work with the probability of good outcomes on each draw.&lt;br&gt;
Following are a few ways you could do the second problem.&lt;br&gt;
(1) Find the number of ways of choosing 2 of the 7 blue balls AND none of the 18 other colors OR 1 of the 7 blue balls AND 1 of the other 18 balls:&lt;br&gt;
{{{C(7,2)*C(18,0)+C(7,1)*C(18,1) = 21*1+7*18 = 21+126 = 147}}}&lt;br&gt;
Then the probability is 147/300.&lt;br&gt;
(2) Find the probability of choosing a blue ball AND then another blue ball, OR choosing a blue ball AND then a different color ball, OR choosing a different color ball and then a blue ball:&lt;br&gt;
{{{(7/25)*(6/24)+(7/25)*(18/24)+(18/25)*(7/24) = (42+126+126)/600 = 294/600 = 147/300.}}}&lt;br&gt;
(3) Find the number of ways of choosing 2 balls which are both NOT blue; convert that number to a probability, and subtract from 1:&lt;br&gt;
{{{C(18,2) = 153}}}; {{{1-153/300 = 147/300}}}&lt;br&gt;
(4) Find the probability of choosing a ball that is not blue AND then another ball that is not blue, and subtract that from 1:&lt;br&gt;
{{{1 - (18/25)*(17/24) = 1 - 306/600 = 1-153/300 = 147/300}}}&lt;br&gt;
I would strongly recommend that you try solving problems like this in at least a couple of different ways.  Seeing that you can use different methods to get the same right answer gives you confidence in the work you are doing.&lt;br&gt;
I will just note a couple of ways you can work the first problem, using methods similar to those above.&lt;br&gt;
(1) Find the number of ways of choosing 1 red AND 1 blue OR 1 red AND 1 green OR 1 blue AND 1 green; add and convert to a probability by dividing by 300.&lt;br&gt;
(2) Find the number of ways of getting 1 red AND 1 of either other color OR of getting 1 blue AND 1 green; convert to a probability as in the other method.&lt;br&gt;
(3) Find the probability of getting a blue AND then a different color, OR getting a red AND then a different color, OR getting a green AND then a different color.&lt;br&gt;
(4) Find the probability of getting 2 blue OR 2 red OR 2 green and subtract from 1.</PRE>