### Instruction: Six green balls and four red balls are in a bag.  A ball is taken from the bag, its color recorded, then placed back in the bag.  A second ball is taken and its color recorded.  What is the probability the two balls are the same color?### Response: Ok, let's start by finding the probability that the first ball is green.
There are six green balls, and a total of ten balls, so the probability is 6/10.
Right. Now let's find the probability that the second ball is green.
Since the first ball is placed back in the bag, there are still six green balls, and a total of ten balls.
So the probability is still 6/10.
And since we need both of these things to happen, we multiply the probabilities, so 6/10 * 6/10 = 36/100.
Now let's do the same thing for red balls.
There are four red balls, and a total of ten balls, so the probability of drawing a red ball is 4/10.
Right. Now let's find the probability that the second ball is red.
Since the first ball is placed back in the bag, there are still four red balls, and a total of ten balls.
So the probability is still 4/10.
And since we need both of these things to happen, we multiply the probabilities, so 4/10 * 4/10 = 16/100.
Now let's add the probabilities of drawing two green balls and drawing two red balls to find the probability of drawing two balls of the same color.
36/100 + 16/100 = 52/100.