Question

A first box contains 2 black and 2 green pens and a second box contains 4 green and 6 red pens. A random pen is taken from the second box and placed in the first, and then a random pen is taken from the first box and placed in the second. What is the probability that the boxes will return to their original color composition?
 

Answer 1

P(red,red) = 6/10 * 1/5
P(green,green) = 4/10 * 3/5
so add them up

Answer 2

I don’t get what u are multiplying with . Why two time red, red.

Answer 3

And what happens with those black pens

Answer 4

P(red,red) means there is a 6/10 chance of getting a red pen out of box #2.
Then, since there is now exactly 1 red out of the 5 pens now in box #1, there is a 1/5 chance of getting it. Since the two draws are independent events, you multiply the probabilities.

similarly for the green draws

who cares about the black pens? We are dealing with the chance of getting both draws the same, and the 1st draw cannot be black.