### Instruction: A bag has 4 red and 6 blue marbles.  A marble is selected and not replaced, then a second is selected.  What is the probability that both are the same color?### Response: This problem is about conditional probability, which means the probability of an event given that another event has occurred.
In this case, the event I want to find the probability of is that both marbles are the same color, given that one has already been selected.
To do this, I need to consider the different possible outcomes for the first marble and how they affect the probability of the second marble.
If the first marble is red, then there are 3 red and 6 blue marbles left, so the probability of getting another red is 3/9.
If the first marble is blue, then there are 4 red and 5 blue marbles left, so the probability of getting another blue is 5/9.
The probability of getting the same color for both marbles is the sum of these two cases, weighted by the probability of each case occurring.
The probability of getting a red marble first is 4/10, and the probability of getting a blue marble first is 6/10.
So the probability of getting the same color for both marbles is (4/10)(3/9) + (6/10)(5/9).
Simplifying the fractions, I get 12/90 + 30/90, which is 42/90 or 7/15.