Need help figuring this with an,explanation

Question

A bag has 4 red marbles and 6 green marbles . You will draw a marble from the bag . if it is red, replace it and draw another marble. If it is green , leave it out and draw another marble . what is the probability that a second marble drawn is green?

Answer 1

P(red,red) = 0.4(0.4) = 0.16 because of replacement of first red

P(red,green) = 0.4(0.6) = 0.24 because of replacement of first red *

 

P(green, red) = 0.6(4/9) = 24/90 because of non-replacement

P(green, green) = 0.6(5/9) = 1/3 because of non-replacement *

 

The sum of all these probabilities is exactly 1.00, of course.

 

P(green, second marble) = sum of above starred (*) probabilities = 0.24 + 1/3 = 43/75 or 0.57333...