finite help math

Question

There are 3 red and 2 white ball in a container. Two balls are taken from the container one after the other without replacement with the color of each ball noted as it is removed. What is the probability that the second ball taken from the container was red?

Answer 1

As we have not restricted the selection of the first ball, the probability of the second ball selected being red is 3/5. The easiest way to see this:| You can just swap the first two balls, so they have to have the same probability. You may consider the following argument more rigorous, but it really isn't.

P(second ball is red) = P(first ball is red)P(second ball is red | first ball is red) + P(first ball is white)P(second ball is red | first ball is white) = 3/5*2/4+2/5*3/4 = 6/20+6/20 = 12/20 = 3/5