bag has five red and seven blue If two marbles are chosen simultaneously from the bag, what is the probability that they will both be red

Answer 1

We have 5 red marbles inside our bag and we want to select two red marbles, which can be done in 5C2 ways. There are 12 marbles inside our bag and to select any two marbles, there are 12C2 ways to do so.

Thus, our desired probability is 5C2/12C2. As 5C2 = 5!/(3!*2!), we have 5C2 = 10 and as 12C2 = 12!/(10!*2!) = 66, our desired probability is 10/66 = 5/33.